library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.5.1     ✔ tibble    3.2.1
## ✔ lubridate 1.9.3     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(gtsummary)
library(emulator)
## Loading required package: mvtnorm
test_df=read_csv('Project_1_data.csv') %>% janitor::clean_names() 
## Rows: 948 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (10): Gender, EthnicGroup, ParentEduc, LunchType, TestPrep, ParentMarita...
## dbl  (4): NrSiblings, MathScore, ReadingScore, WritingScore
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
test_df=test_df %>%  
  mutate(is_first_child=case_when(
    is.na(is_first_child) &nr_siblings==0 ~ 'yes',
    TRUE ~is_first_child
  )) %>% 
        mutate(gender=as.factor(gender),
               ethnic_group=as.factor(ethnic_group),
               parent_educ=as.factor(parent_educ),
               lunch_type=as.factor(lunch_type),
               test_prep=as.factor(test_prep),
               parent_marital_status=as.factor(parent_marital_status),
               practice_sport=as.factor(practice_sport),
               is_first_child=as.factor(is_first_child),
               transport_means=as.factor(transport_means),
               wkly_study_hours=as.factor(wkly_study_hours)) %>% drop_na()
summary(test_df)
##     gender     ethnic_group             parent_educ         lunch_type 
##  female:315   group A: 50   associate's degree:129   free/reduced:207  
##  male  :275   group B:123   bachelor's degree : 71   standard    :383  
##               group C:175   high school       :123                     
##               group D:156   master's degree   : 39                     
##               group E: 86   some college      :116                     
##                             some high school  :112                     
##      test_prep   parent_marital_status   practice_sport is_first_child
##  completed:210   divorced: 93          never    : 69    no :192       
##  none     :380   married :344          regularly:219    yes:398       
##                  single  :138          sometimes:302                  
##                  widowed : 15                                         
##                                                                       
##                                                                       
##   nr_siblings      transport_means wkly_study_hours   math_score    
##  Min.   :0.000   private   :229    < 5   :156       Min.   :  0.00  
##  1st Qu.:1.000   school_bus:361    > 10  :104       1st Qu.: 56.25  
##  Median :2.000                     10-May:330       Median : 67.00  
##  Mean   :2.129                                      Mean   : 66.74  
##  3rd Qu.:3.000                                      3rd Qu.: 78.00  
##  Max.   :7.000                                      Max.   :100.00  
##  reading_score    writing_score   
##  Min.   : 17.00   Min.   : 10.00  
##  1st Qu.: 60.00   1st Qu.: 58.00  
##  Median : 70.00   Median : 69.00  
##  Mean   : 69.87   Mean   : 68.92  
##  3rd Qu.: 81.00   3rd Qu.: 79.00  
##  Max.   :100.00   Max.   :100.00
test_df %>% 
  ggplot(aes(x=math_score))+geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

test_df %>% 
  ggplot(aes(x=reading_score))+geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

test_df %>% 
  ggplot(aes(x=writing_score))+geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

stu_data=table(test_df$gender,test_df$ethnic_group)

chisq.test(stu_data)
## 
##  Pearson's Chi-squared test
## 
## data:  stu_data
## X-squared = 7.211, df = 4, p-value = 0.1251
# Loop through pairs of columns and run the chi-square test

for (i in 1:(11 - 1)) {
  for (j in (i + 1):11) {
    # Get the two columns to test
    col1 <- test_df[[i]]
    col2 <- test_df[[j]]
    
    contingency_table <- table(col1, col2)
    
    # Perform the chi-square test
    chi_test <- chisq.test(contingency_table)
    
    #PRint the results 
    if(chi_test$p.value<.05){
      
      
      cat("Chi-square test for columns", colnames(test_df)[i], "and", colnames(test_df)[j], "\n")
    print(chi_test)
    

    }
    
  }
}
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Chi-square test for columns gender and nr_siblings 
## 
##  Pearson's Chi-squared test
## 
## data:  contingency_table
## X-squared = 15.086, df = 7, p-value = 0.03491
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Chi-square test for columns is_first_child and nr_siblings 
## 
##  Pearson's Chi-squared test
## 
## data:  contingency_table
## X-squared = 45.266, df = 7, p-value = 1.214e-07
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
ggplot(test_df, aes(x = nr_siblings, fill = gender)) +
      geom_bar(position = "fill") +
      labs(y = "Proportion", title = "Pairwise Relationship")

ggplot(test_df, aes(x = nr_siblings, fill = is_first_child)) +
      geom_bar(position = "fill") +
      labs(y = "Proportion", title = "Pairwise Relationship")

Writing Score

df_4_mdl_write=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,writing_score)
full_fit_write=lm(writing_score ~ .^2,data=df_4_mdl_write)
summary(full_fit_write)
## 
## Call:
## lm(formula = writing_score ~ .^2, data = df_4_mdl_write)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -36.097  -6.757   0.000   7.512  25.909 
## 
## Coefficients: (4 not defined because of singularities)
##                                                           Estimate Std. Error
## (Intercept)                                                77.5056    16.5568
## gendermale                                                -11.5459     8.4352
## ethnic_groupgroup B                                       -14.6713    14.2358
## ethnic_groupgroup C                                       -23.6506    13.4300
## ethnic_groupgroup D                                        -6.5467    14.6194
## ethnic_groupgroup E                                        -0.6452    13.7011
## parent_educbachelor's degree                               32.2994    14.9679
## parent_educhigh school                                      8.9108    12.3906
## parent_educmaster's degree                                -13.3428    20.4548
## parent_educsome college                                    -9.2192    12.1578
## parent_educsome high school                                 0.3856    11.7932
## lunch_typestandard                                          3.1104     8.3745
## test_prepnone                                             -18.8143     8.7378
## parent_marital_statusmarried                               16.0430    11.1254
## parent_marital_statussingle                                10.7223    13.3899
## parent_marital_statuswidowed                               43.4838    39.5573
## practice_sportregularly                                   -23.0508    13.3196
## practice_sportsometimes                                   -19.7741    13.2523
## is_first_childyes                                          14.2090     9.5945
## transport_meansschool_bus                                  -3.2352     8.4932
## wkly_study_hours> 10                                      -19.5441    13.0836
## wkly_study_hours10-May                                      1.6614    10.5143
## gendermale:ethnic_groupgroup B                              4.3932     5.3431
## gendermale:ethnic_groupgroup C                              9.3149     5.1384
## gendermale:ethnic_groupgroup D                              5.8109     5.1043
## gendermale:ethnic_groupgroup E                              5.3001     5.6595
## gendermale:parent_educbachelor's degree                    -3.1793     4.4945
## gendermale:parent_educhigh school                           1.0620     3.6653
## gendermale:parent_educmaster's degree                       9.9155     6.2928
## gendermale:parent_educsome college                         -4.1300     3.8491
## gendermale:parent_educsome high school                      0.2529     3.7808
## gendermale:lunch_typestandard                              -1.2039     2.6255
## gendermale:test_prepnone                                   -0.2240     2.6166
## gendermale:parent_marital_statusmarried                    -0.4821     3.7301
## gendermale:parent_marital_statussingle                     -0.1518     4.2288
## gendermale:parent_marital_statuswidowed                     1.2933    18.3113
## gendermale:practice_sportregularly                         -3.0622     4.4464
## gendermale:practice_sportsometimes                         -3.2602     4.4697
## gendermale:is_first_childyes                                3.0435     2.7466
## gendermale:transport_meansschool_bus                       -0.1546     2.5389
## gendermale:wkly_study_hours> 10                            -3.8677     3.9831
## gendermale:wkly_study_hours10-May                          -2.6013     3.0208
## ethnic_groupgroup B:parent_educbachelor's degree           -8.3345    12.4645
## ethnic_groupgroup C:parent_educbachelor's degree           -8.4712    12.4445
## ethnic_groupgroup D:parent_educbachelor's degree           -9.6856    12.3505
## ethnic_groupgroup E:parent_educbachelor's degree          -16.9547    14.0557
## ethnic_groupgroup B:parent_educhigh school                -16.1825     7.8036
## ethnic_groupgroup C:parent_educhigh school                -10.7952     7.5005
## ethnic_groupgroup D:parent_educhigh school                 -7.6467     7.6256
## ethnic_groupgroup E:parent_educhigh school                -11.4328     8.4924
## ethnic_groupgroup B:parent_educmaster's degree              4.9001    14.9754
## ethnic_groupgroup C:parent_educmaster's degree             -7.4679    13.9097
## ethnic_groupgroup D:parent_educmaster's degree              2.9024    14.1310
## ethnic_groupgroup E:parent_educmaster's degree              1.3629    14.8684
## ethnic_groupgroup B:parent_educsome college                 3.2143     8.6301
## ethnic_groupgroup C:parent_educsome college                 5.9797     8.1460
## ethnic_groupgroup D:parent_educsome college                 9.5674     8.4844
## ethnic_groupgroup E:parent_educsome college                 2.6023     8.5774
## ethnic_groupgroup B:parent_educsome high school           -17.7650     8.2716
## ethnic_groupgroup C:parent_educsome high school           -10.3880     7.7610
## ethnic_groupgroup D:parent_educsome high school            -6.6709     7.8120
## ethnic_groupgroup E:parent_educsome high school            -4.3383     8.3877
## ethnic_groupgroup B:lunch_typestandard                      3.1284     5.5561
## ethnic_groupgroup C:lunch_typestandard                      6.9223     5.3886
## ethnic_groupgroup D:lunch_typestandard                      3.8322     5.3042
## ethnic_groupgroup E:lunch_typestandard                     -0.1953     6.1469
## ethnic_groupgroup B:test_prepnone                           2.4242     5.6685
## ethnic_groupgroup C:test_prepnone                           6.4991     5.3175
## ethnic_groupgroup D:test_prepnone                           4.2882     5.3281
## ethnic_groupgroup E:test_prepnone                          10.4184     5.7998
## ethnic_groupgroup B:parent_marital_statusmarried            4.0514     7.6528
## ethnic_groupgroup C:parent_marital_statusmarried           -0.2301     7.0469
## ethnic_groupgroup D:parent_marital_statusmarried          -10.9053     6.9504
## ethnic_groupgroup E:parent_marital_statusmarried           -4.3960     7.6897
## ethnic_groupgroup B:parent_marital_statussingle            10.5415     9.0607
## ethnic_groupgroup C:parent_marital_statussingle             2.1275     8.5665
## ethnic_groupgroup D:parent_marital_statussingle            -2.6676     8.2778
## ethnic_groupgroup E:parent_marital_statussingle             3.1117     9.5410
## ethnic_groupgroup B:parent_marital_statuswidowed           73.8433   101.3778
## ethnic_groupgroup C:parent_marital_statuswidowed          114.3340    82.3923
## ethnic_groupgroup D:parent_marital_statuswidowed           12.1039    83.0580
## ethnic_groupgroup E:parent_marital_statuswidowed                NA         NA
## ethnic_groupgroup B:practice_sportregularly                14.5020    10.1514
## ethnic_groupgroup C:practice_sportregularly                15.9609    10.0599
## ethnic_groupgroup D:practice_sportregularly                11.8248    11.2295
## ethnic_groupgroup E:practice_sportregularly                12.9574    10.2802
## ethnic_groupgroup B:practice_sportsometimes                12.6309    10.8289
## ethnic_groupgroup C:practice_sportsometimes                22.0758    10.5328
## ethnic_groupgroup D:practice_sportsometimes                12.1147    11.6115
## ethnic_groupgroup E:practice_sportsometimes                12.5339    10.5863
## ethnic_groupgroup B:is_first_childyes                       9.7409     5.6253
## ethnic_groupgroup C:is_first_childyes                       3.4474     5.3065
## ethnic_groupgroup D:is_first_childyes                       1.8617     5.3681
## ethnic_groupgroup E:is_first_childyes                       2.7052     6.0462
## ethnic_groupgroup B:transport_meansschool_bus              -7.4751     5.6284
## ethnic_groupgroup C:transport_meansschool_bus             -11.2746     5.1972
## ethnic_groupgroup D:transport_meansschool_bus              -5.1875     5.1920
## ethnic_groupgroup E:transport_meansschool_bus             -12.0724     6.1289
## ethnic_groupgroup B:wkly_study_hours> 10                   -5.9602     9.5818
## ethnic_groupgroup C:wkly_study_hours> 10                    1.9360     9.4624
## ethnic_groupgroup D:wkly_study_hours> 10                    6.7581     9.4492
## ethnic_groupgroup E:wkly_study_hours> 10                    0.4986    10.2937
## ethnic_groupgroup B:wkly_study_hours10-May                 -5.8066     8.0474
## ethnic_groupgroup C:wkly_study_hours10-May                  1.8457     7.8744
## ethnic_groupgroup D:wkly_study_hours10-May                  2.9555     8.0075
## ethnic_groupgroup E:wkly_study_hours10-May                 -1.4251     8.6215
## parent_educbachelor's degree:lunch_typestandard             0.9925     4.8362
## parent_educhigh school:lunch_typestandard                   0.9740     3.9027
## parent_educmaster's degree:lunch_typestandard               6.9772     7.1530
## parent_educsome college:lunch_typestandard                  5.3543     3.9343
## parent_educsome high school:lunch_typestandard              5.7895     4.0754
## parent_educbachelor's degree:test_prepnone                 -1.3131     4.4623
## parent_educhigh school:test_prepnone                        1.8447     4.2737
## parent_educmaster's degree:test_prepnone                   -2.3089     7.6077
## parent_educsome college:test_prepnone                      -1.8819     4.0056
## parent_educsome high school:test_prepnone                   2.4708     3.8740
## parent_educbachelor's degree:parent_marital_statusmarried -17.2754     7.9642
## parent_educhigh school:parent_marital_statusmarried         2.5731     5.6012
## parent_educmaster's degree:parent_marital_statusmarried     4.5317     8.1036
## parent_educsome college:parent_marital_statusmarried       -4.8368     5.5157
## parent_educsome high school:parent_marital_statusmarried   -3.8229     5.4356
## parent_educbachelor's degree:parent_marital_statussingle  -16.6290     8.5852
## parent_educhigh school:parent_marital_statussingle          6.4988     6.1186
## parent_educmaster's degree:parent_marital_statussingle      1.5045     8.6504
## parent_educsome college:parent_marital_statussingle        -4.6580     6.1430
## parent_educsome high school:parent_marital_statussingle    -3.7573     6.0684
## parent_educbachelor's degree:parent_marital_statuswidowed -20.6113    84.4043
## parent_educhigh school:parent_marital_statuswidowed       -74.8517    92.8678
## parent_educmaster's degree:parent_marital_statuswidowed   -98.2733    48.6482
## parent_educsome college:parent_marital_statuswidowed      -87.5058    60.9959
## parent_educsome high school:parent_marital_statuswidowed  -61.8441    73.1065
## parent_educbachelor's degree:practice_sportregularly        1.8608     8.2226
## parent_educhigh school:practice_sportregularly            -10.9775     7.0762
## parent_educmaster's degree:practice_sportregularly          1.5289     9.9993
## parent_educsome college:practice_sportregularly            -0.1518     7.1960
## parent_educsome high school:practice_sportregularly        -3.2753     6.9492
## parent_educbachelor's degree:practice_sportsometimes       -8.3616     7.8902
## parent_educhigh school:practice_sportsometimes            -10.1532     6.7020
## parent_educmaster's degree:practice_sportsometimes          6.4978     8.3297
## parent_educsome college:practice_sportsometimes             2.7525     6.9253
## parent_educsome high school:practice_sportsometimes        -1.5359     6.5116
## parent_educbachelor's degree:is_first_childyes              5.9213     4.8829
## parent_educhigh school:is_first_childyes                    8.2978     4.1681
## parent_educmaster's degree:is_first_childyes                4.0575     7.2904
## parent_educsome college:is_first_childyes                  11.3686     4.0703
## parent_educsome high school:is_first_childyes               6.6910     4.0992
## parent_educbachelor's degree:transport_meansschool_bus      2.9865     4.8745
## parent_educhigh school:transport_meansschool_bus            4.2359     3.8916
## parent_educmaster's degree:transport_meansschool_bus        7.9641     6.0004
## parent_educsome college:transport_meansschool_bus           2.9693     3.9628
## parent_educsome high school:transport_meansschool_bus       6.6974     4.0323
## parent_educbachelor's degree:wkly_study_hours> 10         -10.0969     7.1918
## parent_educhigh school:wkly_study_hours> 10                -8.9401     5.9867
## parent_educmaster's degree:wkly_study_hours> 10            -0.4929    12.9542
## parent_educsome college:wkly_study_hours> 10               -7.9346     6.0260
## parent_educsome high school:wkly_study_hours> 10           -9.2345     6.1375
## parent_educbachelor's degree:wkly_study_hours10-May        -3.0831     4.9986
## parent_educhigh school:wkly_study_hours10-May             -11.4380     4.6604
## parent_educmaster's degree:wkly_study_hours10-May          -2.4586     6.6645
## parent_educsome college:wkly_study_hours10-May             -4.9978     4.7455
## parent_educsome high school:wkly_study_hours10-May         -9.0404     5.0069
## lunch_typestandard:test_prepnone                           -2.5751     2.9272
## lunch_typestandard:parent_marital_statusmarried            -7.6602     3.8303
## lunch_typestandard:parent_marital_statussingle             -4.8424     4.4351
## lunch_typestandard:parent_marital_statuswidowed            -0.3401    75.8094
## lunch_typestandard:practice_sportregularly                  9.3167     5.0489
## lunch_typestandard:practice_sportsometimes                 11.9692     4.8670
## lunch_typestandard:is_first_childyes                       -3.2287     2.9659
## lunch_typestandard:transport_meansschool_bus               -2.5877     2.7218
## lunch_typestandard:wkly_study_hours> 10                     6.6183     4.1533
## lunch_typestandard:wkly_study_hours10-May                   0.2394     3.1068
## test_prepnone:parent_marital_statusmarried                  1.3790     3.8961
## test_prepnone:parent_marital_statussingle                  -2.2649     4.4856
## test_prepnone:parent_marital_statuswidowed                -56.1241    39.6071
## test_prepnone:practice_sportregularly                       2.1756     4.8701
## test_prepnone:practice_sportsometimes                       4.8914     4.7728
## test_prepnone:is_first_childyes                            -0.6209     2.9395
## test_prepnone:transport_meansschool_bus                     2.2476     2.6727
## test_prepnone:wkly_study_hours> 10                         -2.8715     4.1954
## test_prepnone:wkly_study_hours10-May                        2.5604     3.3110
## parent_marital_statusmarried:practice_sportregularly        4.6749     6.2606
## parent_marital_statussingle:practice_sportregularly        -3.7080     8.1872
## parent_marital_statuswidowed:practice_sportregularly       -2.7432    80.1680
## parent_marital_statusmarried:practice_sportsometimes        2.9212     6.1741
## parent_marital_statussingle:practice_sportsometimes        -4.2724     8.0039
## parent_marital_statuswidowed:practice_sportsometimes            NA         NA
## parent_marital_statusmarried:is_first_childyes            -15.6491     4.6054
## parent_marital_statussingle:is_first_childyes              -7.5649     5.1042
## parent_marital_statuswidowed:is_first_childyes             39.8253    28.4103
## parent_marital_statusmarried:transport_meansschool_bus      4.5994     3.8033
## parent_marital_statussingle:transport_meansschool_bus       0.4248     4.3343
## parent_marital_statuswidowed:transport_meansschool_bus    -24.3230    18.4632
## parent_marital_statusmarried:wkly_study_hours> 10          19.5443     5.9414
## parent_marital_statussingle:wkly_study_hours> 10           25.1083     6.6075
## parent_marital_statuswidowed:wkly_study_hours> 10               NA         NA
## parent_marital_statusmarried:wkly_study_hours10-May         5.3774     4.3617
## parent_marital_statussingle:wkly_study_hours10-May          7.7403     4.8173
## parent_marital_statuswidowed:wkly_study_hours10-May             NA         NA
## practice_sportregularly:is_first_childyes                  -5.8879     5.6556
## practice_sportsometimes:is_first_childyes                  -7.2854     5.5185
## practice_sportregularly:transport_meansschool_bus           9.5708     4.7258
## practice_sportsometimes:transport_meansschool_bus           6.1714     4.5868
## practice_sportregularly:wkly_study_hours> 10                5.1152     6.7000
## practice_sportsometimes:wkly_study_hours> 10                3.1990     6.5717
## practice_sportregularly:wkly_study_hours10-May              6.9393     5.1561
## practice_sportsometimes:wkly_study_hours10-May             -0.3073     5.0837
## is_first_childyes:transport_meansschool_bus                -3.0863     2.8768
## is_first_childyes:wkly_study_hours> 10                      3.0112     4.3247
## is_first_childyes:wkly_study_hours10-May                   -2.5351     3.2646
## transport_meansschool_bus:wkly_study_hours> 10              2.0199     4.1559
## transport_meansschool_bus:wkly_study_hours10-May            1.8077     3.0009
##                                                           t value Pr(>|t|)    
## (Intercept)                                                 4.681 3.96e-06 ***
## gendermale                                                 -1.369 0.171871    
## ethnic_groupgroup B                                        -1.031 0.303382    
## ethnic_groupgroup C                                        -1.761 0.079032 .  
## ethnic_groupgroup D                                        -0.448 0.654545    
## ethnic_groupgroup E                                        -0.047 0.962465    
## parent_educbachelor's degree                                2.158 0.031556 *  
## parent_educhigh school                                      0.719 0.472484    
## parent_educmaster's degree                                 -0.652 0.514593    
## parent_educsome college                                    -0.758 0.448740    
## parent_educsome high school                                 0.033 0.973933    
## lunch_typestandard                                          0.371 0.710536    
## test_prepnone                                              -2.153 0.031925 *  
## parent_marital_statusmarried                                1.442 0.150115    
## parent_marital_statussingle                                 0.801 0.423760    
## parent_marital_statuswidowed                                1.099 0.272344    
## practice_sportregularly                                    -1.731 0.084330 .  
## practice_sportsometimes                                    -1.492 0.136489    
## is_first_childyes                                           1.481 0.139442    
## transport_meansschool_bus                                  -0.381 0.703477    
## wkly_study_hours> 10                                       -1.494 0.136054    
## wkly_study_hours10-May                                      0.158 0.874530    
## gendermale:ethnic_groupgroup B                              0.822 0.411462    
## gendermale:ethnic_groupgroup C                              1.813 0.070644 .  
## gendermale:ethnic_groupgroup D                              1.138 0.255657    
## gendermale:ethnic_groupgroup E                              0.937 0.349605    
## gendermale:parent_educbachelor's degree                    -0.707 0.479756    
## gendermale:parent_educhigh school                           0.290 0.772172    
## gendermale:parent_educmaster's degree                       1.576 0.115922    
## gendermale:parent_educsome college                         -1.073 0.283958    
## gendermale:parent_educsome high school                      0.067 0.946710    
## gendermale:lunch_typestandard                              -0.459 0.646819    
## gendermale:test_prepnone                                   -0.086 0.931825    
## gendermale:parent_marital_statusmarried                    -0.129 0.897232    
## gendermale:parent_marital_statussingle                     -0.036 0.971377    
## gendermale:parent_marital_statuswidowed                     0.071 0.943731    
## gendermale:practice_sportregularly                         -0.689 0.491428    
## gendermale:practice_sportsometimes                         -0.729 0.466204    
## gendermale:is_first_childyes                                1.108 0.268521    
## gendermale:transport_meansschool_bus                       -0.061 0.951464    
## gendermale:wkly_study_hours> 10                            -0.971 0.332150    
## gendermale:wkly_study_hours10-May                          -0.861 0.389706    
## ethnic_groupgroup B:parent_educbachelor's degree           -0.669 0.504113    
## ethnic_groupgroup C:parent_educbachelor's degree           -0.681 0.496462    
## ethnic_groupgroup D:parent_educbachelor's degree           -0.784 0.433391    
## ethnic_groupgroup E:parent_educbachelor's degree           -1.206 0.228465    
## ethnic_groupgroup B:parent_educhigh school                 -2.074 0.038774 *  
## ethnic_groupgroup C:parent_educhigh school                 -1.439 0.150891    
## ethnic_groupgroup D:parent_educhigh school                 -1.003 0.316603    
## ethnic_groupgroup E:parent_educhigh school                 -1.346 0.179020    
## ethnic_groupgroup B:parent_educmaster's degree              0.327 0.743685    
## ethnic_groupgroup C:parent_educmaster's degree             -0.537 0.591656    
## ethnic_groupgroup D:parent_educmaster's degree              0.205 0.837375    
## ethnic_groupgroup E:parent_educmaster's degree              0.092 0.927013    
## ethnic_groupgroup B:parent_educsome college                 0.372 0.709764    
## ethnic_groupgroup C:parent_educsome college                 0.734 0.463358    
## ethnic_groupgroup D:parent_educsome college                 1.128 0.260175    
## ethnic_groupgroup E:parent_educsome college                 0.303 0.761758    
## ethnic_groupgroup B:parent_educsome high school            -2.148 0.032364 *  
## ethnic_groupgroup C:parent_educsome high school            -1.338 0.181530    
## ethnic_groupgroup D:parent_educsome high school            -0.854 0.393676    
## ethnic_groupgroup E:parent_educsome high school            -0.517 0.605302    
## ethnic_groupgroup B:lunch_typestandard                      0.563 0.573723    
## ethnic_groupgroup C:lunch_typestandard                      1.285 0.199701    
## ethnic_groupgroup D:lunch_typestandard                      0.722 0.470435    
## ethnic_groupgroup E:lunch_typestandard                     -0.032 0.974675    
## ethnic_groupgroup B:test_prepnone                           0.428 0.669136    
## ethnic_groupgroup C:test_prepnone                           1.222 0.222374    
## ethnic_groupgroup D:test_prepnone                           0.805 0.421423    
## ethnic_groupgroup E:test_prepnone                           1.796 0.073229 .  
## ethnic_groupgroup B:parent_marital_statusmarried            0.529 0.596832    
## ethnic_groupgroup C:parent_marital_statusmarried           -0.033 0.973967    
## ethnic_groupgroup D:parent_marital_statusmarried           -1.569 0.117469    
## ethnic_groupgroup E:parent_marital_statusmarried           -0.572 0.567873    
## ethnic_groupgroup B:parent_marital_statussingle             1.163 0.245378    
## ethnic_groupgroup C:parent_marital_statussingle             0.248 0.803994    
## ethnic_groupgroup D:parent_marital_statussingle            -0.322 0.747428    
## ethnic_groupgroup E:parent_marital_statussingle             0.326 0.744500    
## ethnic_groupgroup B:parent_marital_statuswidowed            0.728 0.466816    
## ethnic_groupgroup C:parent_marital_statuswidowed            1.388 0.166042    
## ethnic_groupgroup D:parent_marital_statuswidowed            0.146 0.884212    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                 1.429 0.153942    
## ethnic_groupgroup C:practice_sportregularly                 1.587 0.113432    
## ethnic_groupgroup D:practice_sportregularly                 1.053 0.293000    
## ethnic_groupgroup E:practice_sportregularly                 1.260 0.208281    
## ethnic_groupgroup B:practice_sportsometimes                 1.166 0.244177    
## ethnic_groupgroup C:practice_sportsometimes                 2.096 0.036745 *  
## ethnic_groupgroup D:practice_sportsometimes                 1.043 0.297450    
## ethnic_groupgroup E:practice_sportsometimes                 1.184 0.237159    
## ethnic_groupgroup B:is_first_childyes                       1.732 0.084147 .  
## ethnic_groupgroup C:is_first_childyes                       0.650 0.516308    
## ethnic_groupgroup D:is_first_childyes                       0.347 0.728926    
## ethnic_groupgroup E:is_first_childyes                       0.447 0.654819    
## ethnic_groupgroup B:transport_meansschool_bus              -1.328 0.184937    
## ethnic_groupgroup C:transport_meansschool_bus              -2.169 0.030669 *  
## ethnic_groupgroup D:transport_meansschool_bus              -0.999 0.318358    
## ethnic_groupgroup E:transport_meansschool_bus              -1.970 0.049590 *  
## ethnic_groupgroup B:wkly_study_hours> 10                   -0.622 0.534294    
## ethnic_groupgroup C:wkly_study_hours> 10                    0.205 0.837996    
## ethnic_groupgroup D:wkly_study_hours> 10                    0.715 0.474919    
## ethnic_groupgroup E:wkly_study_hours> 10                    0.048 0.961392    
## ethnic_groupgroup B:wkly_study_hours10-May                 -0.722 0.471008    
## ethnic_groupgroup C:wkly_study_hours10-May                  0.234 0.814802    
## ethnic_groupgroup D:wkly_study_hours10-May                  0.369 0.712263    
## ethnic_groupgroup E:wkly_study_hours10-May                 -0.165 0.868800    
## parent_educbachelor's degree:lunch_typestandard             0.205 0.837509    
## parent_educhigh school:lunch_typestandard                   0.250 0.803050    
## parent_educmaster's degree:lunch_typestandard               0.975 0.329964    
## parent_educsome college:lunch_typestandard                  1.361 0.174329    
## parent_educsome high school:lunch_typestandard              1.421 0.156247    
## parent_educbachelor's degree:test_prepnone                 -0.294 0.768711    
## parent_educhigh school:test_prepnone                        0.432 0.666242    
## parent_educmaster's degree:test_prepnone                   -0.303 0.761677    
## parent_educsome college:test_prepnone                      -0.470 0.638759    
## parent_educsome high school:test_prepnone                   0.638 0.523982    
## parent_educbachelor's degree:parent_marital_statusmarried  -2.169 0.030688 *  
## parent_educhigh school:parent_marital_statusmarried         0.459 0.646215    
## parent_educmaster's degree:parent_marital_statusmarried     0.559 0.576337    
## parent_educsome college:parent_marital_statusmarried       -0.877 0.381080    
## parent_educsome high school:parent_marital_statusmarried   -0.703 0.482292    
## parent_educbachelor's degree:parent_marital_statussingle   -1.937 0.053489 .  
## parent_educhigh school:parent_marital_statussingle          1.062 0.288837    
## parent_educmaster's degree:parent_marital_statussingle      0.174 0.862019    
## parent_educsome college:parent_marital_statussingle        -0.758 0.448762    
## parent_educsome high school:parent_marital_statussingle    -0.619 0.536181    
## parent_educbachelor's degree:parent_marital_statuswidowed  -0.244 0.807209    
## parent_educhigh school:parent_marital_statuswidowed        -0.806 0.420742    
## parent_educmaster's degree:parent_marital_statuswidowed    -2.020 0.044071 *  
## parent_educsome college:parent_marital_statuswidowed       -1.435 0.152213    
## parent_educsome high school:parent_marital_statuswidowed   -0.846 0.398112    
## parent_educbachelor's degree:practice_sportregularly        0.226 0.821088    
## parent_educhigh school:practice_sportregularly             -1.551 0.121650    
## parent_educmaster's degree:practice_sportregularly          0.153 0.878559    
## parent_educsome college:practice_sportregularly            -0.021 0.983182    
## parent_educsome high school:practice_sportregularly        -0.471 0.637680    
## parent_educbachelor's degree:practice_sportsometimes       -1.060 0.289930    
## parent_educhigh school:practice_sportsometimes             -1.515 0.130609    
## parent_educmaster's degree:practice_sportsometimes          0.780 0.435832    
## parent_educsome college:practice_sportsometimes             0.397 0.691259    
## parent_educsome high school:practice_sportsometimes        -0.236 0.813660    
## parent_educbachelor's degree:is_first_childyes              1.213 0.226003    
## parent_educhigh school:is_first_childyes                    1.991 0.047213 *  
## parent_educmaster's degree:is_first_childyes                0.557 0.578162    
## parent_educsome college:is_first_childyes                   2.793 0.005483 ** 
## parent_educsome high school:is_first_childyes               1.632 0.103442    
## parent_educbachelor's degree:transport_meansschool_bus      0.613 0.540462    
## parent_educhigh school:transport_meansschool_bus            1.088 0.277080    
## parent_educmaster's degree:transport_meansschool_bus        1.327 0.185211    
## parent_educsome college:transport_meansschool_bus           0.749 0.454133    
## parent_educsome high school:transport_meansschool_bus       1.661 0.097541 .  
## parent_educbachelor's degree:wkly_study_hours> 10          -1.404 0.161148    
## parent_educhigh school:wkly_study_hours> 10                -1.493 0.136173    
## parent_educmaster's degree:wkly_study_hours> 10            -0.038 0.969667    
## parent_educsome college:wkly_study_hours> 10               -1.317 0.188716    
## parent_educsome high school:wkly_study_hours> 10           -1.505 0.133251    
## parent_educbachelor's degree:wkly_study_hours10-May        -0.617 0.537741    
## parent_educhigh school:wkly_study_hours10-May              -2.454 0.014560 *  
## parent_educmaster's degree:wkly_study_hours10-May          -0.369 0.712402    
## parent_educsome college:wkly_study_hours10-May             -1.053 0.292924    
## parent_educsome high school:wkly_study_hours10-May         -1.806 0.071766 .  
## lunch_typestandard:test_prepnone                           -0.880 0.379567    
## lunch_typestandard:parent_marital_statusmarried            -2.000 0.046216 *  
## lunch_typestandard:parent_marital_statussingle             -1.092 0.275596    
## lunch_typestandard:parent_marital_statuswidowed            -0.004 0.996423    
## lunch_typestandard:practice_sportregularly                  1.845 0.065767 .  
## lunch_typestandard:practice_sportsometimes                  2.459 0.014363 *  
## lunch_typestandard:is_first_childyes                       -1.089 0.277020    
## lunch_typestandard:transport_meansschool_bus               -0.951 0.342335    
## lunch_typestandard:wkly_study_hours> 10                     1.593 0.111876    
## lunch_typestandard:wkly_study_hours10-May                   0.077 0.938623    
## test_prepnone:parent_marital_statusmarried                  0.354 0.723573    
## test_prepnone:parent_marital_statussingle                  -0.505 0.613893    
## test_prepnone:parent_marital_statuswidowed                 -1.417 0.157290    
## test_prepnone:practice_sportregularly                       0.447 0.655333    
## test_prepnone:practice_sportsometimes                       1.025 0.306088    
## test_prepnone:is_first_childyes                            -0.211 0.832828    
## test_prepnone:transport_meansschool_bus                     0.841 0.400913    
## test_prepnone:wkly_study_hours> 10                         -0.684 0.494109    
## test_prepnone:wkly_study_hours10-May                        0.773 0.439827    
## parent_marital_statusmarried:practice_sportregularly        0.747 0.455689    
## parent_marital_statussingle:practice_sportregularly        -0.453 0.650870    
## parent_marital_statuswidowed:practice_sportregularly       -0.034 0.972721    
## parent_marital_statusmarried:practice_sportsometimes        0.473 0.636383    
## parent_marital_statussingle:practice_sportsometimes        -0.534 0.593797    
## parent_marital_statuswidowed:practice_sportsometimes           NA       NA    
## parent_marital_statusmarried:is_first_childyes             -3.398 0.000750 ***
## parent_marital_statussingle:is_first_childyes              -1.482 0.139140    
## parent_marital_statuswidowed:is_first_childyes              1.402 0.161788    
## parent_marital_statusmarried:transport_meansschool_bus      1.209 0.227285    
## parent_marital_statussingle:transport_meansschool_bus       0.098 0.921980    
## parent_marital_statuswidowed:transport_meansschool_bus     -1.317 0.188500    
## parent_marital_statusmarried:wkly_study_hours> 10           3.289 0.001097 ** 
## parent_marital_statussingle:wkly_study_hours> 10            3.800 0.000168 ***
## parent_marital_statuswidowed:wkly_study_hours> 10              NA       NA    
## parent_marital_statusmarried:wkly_study_hours10-May         1.233 0.218380    
## parent_marital_statussingle:wkly_study_hours10-May          1.607 0.108933    
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## practice_sportregularly:is_first_childyes                  -1.041 0.298498    
## practice_sportsometimes:is_first_childyes                  -1.320 0.187560    
## practice_sportregularly:transport_meansschool_bus           2.025 0.043539 *  
## practice_sportsometimes:transport_meansschool_bus           1.345 0.179276    
## practice_sportregularly:wkly_study_hours> 10                0.763 0.445653    
## practice_sportsometimes:wkly_study_hours> 10                0.487 0.626687    
## practice_sportregularly:wkly_study_hours10-May              1.346 0.179149    
## practice_sportsometimes:wkly_study_hours10-May             -0.060 0.951832    
## is_first_childyes:transport_meansschool_bus                -1.073 0.284019    
## is_first_childyes:wkly_study_hours> 10                      0.696 0.486682    
## is_first_childyes:wkly_study_hours10-May                   -0.777 0.437906    
## transport_meansschool_bus:wkly_study_hours> 10              0.486 0.627215    
## transport_meansschool_bus:wkly_study_hours10-May            0.602 0.547281    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.42 on 383 degrees of freedom
## Multiple R-squared:  0.5844, Adjusted R-squared:  0.3608 
## F-statistic: 2.614 on 206 and 383 DF,  p-value: 2.56e-16
stepwise_model_write <- step(full_fit_write, direction = "both", trace = 1)
## Start:  AIC=3131.41
## writing_score ~ (gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours)^2
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:test_prep                   5     245.4 59282 3123.9
## - ethnic_group:parent_educ               20    3361.8 62398 3124.1
## - gender:parent_marital_status            3       4.9 59041 3125.5
## - parent_educ:wkly_study_hours           10    1468.0 60504 3125.9
## - ethnic_group:wkly_study_hours           8    1092.4 60129 3126.2
## - parent_educ:transport_means             5     547.3 59583 3126.9
## - parent_marital_status:practice_sport    4     348.1 59384 3126.9
## - parent_educ:lunch_type                  5     600.2 59636 3127.4
## - transport_means:wkly_study_hours        2      63.5 59100 3128.1
## - gender:practice_sport                   2      85.6 59122 3128.3
## - ethnic_group:lunch_type                 4     513.8 59550 3128.5
## - parent_educ:parent_marital_status      13    2409.8 61446 3129.0
## - gender:wkly_study_hours                 2     167.8 59204 3129.1
## - gender:transport_means                  1       0.6 59037 3129.4
## - gender:test_prep                        1       1.1 59037 3129.4
## - test_prep:is_first_child                1       6.9 59043 3129.5
## - test_prep:parent_marital_status         2     211.7 59248 3129.5
## - gender:lunch_type                       1      32.4 59069 3129.7
## - test_prep:practice_sport                2     244.8 59281 3129.8
## - gender:ethnic_group                     4     652.4 59689 3129.9
## - gender:parent_educ                      5     856.7 59893 3129.9
## - practice_sport:is_first_child           2     277.0 59313 3130.2
## - test_prep:transport_means               1     109.0 59145 3130.5
## - lunch_type:test_prep                    1     119.3 59155 3130.6
## - lunch_type:transport_means              1     139.3 59176 3130.8
## - is_first_child:wkly_study_hours         2     340.9 59377 3130.8
## - ethnic_group:is_first_child             4     746.0 59782 3130.8
## - ethnic_group:test_prep                  4     757.2 59793 3130.9
## - is_first_child:transport_means          1     177.4 59214 3131.2
## - lunch_type:is_first_child               1     182.7 59219 3131.2
## - ethnic_group:practice_sport             8    1610.3 60646 3131.3
## - gender:is_first_child                   1     189.3 59225 3131.3
## - test_prep:wkly_study_hours              2     400.5 59437 3131.4
## <none>                                                59036 3131.4
## - parent_educ:practice_sport             10    2078.2 61114 3131.8
## - lunch_type:wkly_study_hours             2     509.7 59546 3132.5
## - parent_marital_status:transport_means   3     755.0 59791 3132.9
## - ethnic_group:parent_marital_status      9    1983.9 61020 3132.9
## - practice_sport:wkly_study_hours         4     995.1 60031 3133.3
## - lunch_type:parent_marital_status        2     650.3 59687 3133.9
## - practice_sport:transport_means          2     679.6 59716 3134.2
## - ethnic_group:transport_means            4    1108.7 60145 3134.4
## - parent_educ:is_first_child              5    1316.0 60352 3134.4
## - lunch_type:practice_sport               2     950.1 59986 3136.8
## - parent_marital_status:wkly_study_hours  4    2324.9 61361 3146.2
## - parent_marital_status:is_first_child    2    2312.7 61349 3150.1
## 
## Step:  AIC=3123.86
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_educ               20    3285.4 62567 3115.7
## - gender:parent_marital_status            3       7.5 59289 3117.9
## - ethnic_group:wkly_study_hours           8    1092.3 60374 3118.6
## - parent_marital_status:practice_sport    4     343.6 59625 3119.3
## - parent_educ:wkly_study_hours           10    1612.0 60894 3119.7
## - parent_educ:lunch_type                  5     596.6 59878 3119.8
## - parent_educ:transport_means             5     601.4 59883 3119.8
## - transport_means:wkly_study_hours        2      57.6 59339 3120.4
## - gender:practice_sport                   2      72.1 59354 3120.6
## - ethnic_group:lunch_type                 4     535.1 59817 3121.2
## - parent_educ:parent_marital_status      13    2393.4 61675 3121.2
## - gender:wkly_study_hours                 2     180.9 59462 3121.7
## - test_prep:parent_marital_status         2     184.5 59466 3121.7
## - gender:test_prep                        1       0.0 59282 3121.9
## - gender:transport_means                  1       1.8 59283 3121.9
## - test_prep:practice_sport                2     207.8 59489 3121.9
## - test_prep:is_first_child                1      10.7 59292 3122.0
## - gender:ethnic_group                     4     627.6 59909 3122.1
## - gender:lunch_type                       1      24.7 59306 3122.1
## - ethnic_group:test_prep                  4     639.2 59921 3122.2
## - gender:parent_educ                      5     892.7 60174 3122.7
## - test_prep:transport_means               1      98.8 59380 3122.8
## - is_first_child:wkly_study_hours         2     302.5 59584 3122.9
## - lunch_type:test_prep                    1     116.0 59398 3123.0
## - practice_sport:is_first_child           2     323.8 59605 3123.1
## - lunch_type:transport_means              1     133.6 59415 3123.2
## - gender:is_first_child                   1     166.6 59448 3123.5
## - ethnic_group:practice_sport             8    1607.5 60889 3123.6
## - ethnic_group:is_first_child             4     790.6 60072 3123.7
## - lunch_type:is_first_child               1     199.8 59481 3123.8
## <none>                                                59282 3123.9
## - is_first_child:transport_means          1     217.5 59499 3124.0
## - test_prep:wkly_study_hours              2     441.6 59723 3124.2
## - ethnic_group:parent_marital_status      9    1922.8 61204 3124.7
## - parent_educ:practice_sport             10    2157.5 61439 3124.9
## - lunch_type:wkly_study_hours             2     549.6 59831 3125.3
## - parent_marital_status:transport_means   3     758.5 60040 3125.4
## - lunch_type:parent_marital_status        2     587.8 59869 3125.7
## - practice_sport:wkly_study_hours         4    1017.6 60299 3125.9
## - ethnic_group:transport_means            4    1123.4 60405 3126.9
## - practice_sport:transport_means          2     729.9 60011 3127.1
## - parent_educ:is_first_child              5    1429.3 60711 3127.9
## - lunch_type:practice_sport               2     950.3 60232 3129.2
## + parent_educ:test_prep                   5     245.4 59036 3131.4
## - parent_marital_status:wkly_study_hours  4    2425.4 61707 3139.5
## - parent_marital_status:is_first_child    2    2368.4 61650 3143.0
## 
## Step:  AIC=3115.68
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:wkly_study_hours           8     838.3 63405 3107.5
## - parent_educ:wkly_study_hours           10    1310.7 63878 3107.9
## - gender:parent_marital_status            3      12.5 62579 3109.8
## - parent_educ:lunch_type                  5     510.3 63077 3110.5
## - parent_marital_status:practice_sport    4     360.8 62928 3111.1
## - ethnic_group:practice_sport             8    1247.6 63815 3111.3
## - parent_educ:transport_means             5     641.0 63208 3111.7
## - gender:ethnic_group                     4     522.4 63089 3112.6
## - ethnic_group:test_prep                  4     527.3 63094 3112.6
## - test_prep:parent_marital_status         2     142.9 62710 3113.0
## - transport_means:wkly_study_hours        2     159.6 62726 3113.2
## - gender:wkly_study_hours                 2     161.7 62729 3113.2
## - gender:parent_educ                      5     828.0 63395 3113.4
## - gender:practice_sport                   2     190.3 62757 3113.5
## - is_first_child:wkly_study_hours         2     192.2 62759 3113.5
## - gender:transport_means                  1       0.9 62568 3113.7
## - gender:test_prep                        1       1.5 62568 3113.7
## - lunch_type:test_prep                    1       5.1 62572 3113.7
## - gender:lunch_type                       1       8.8 62576 3113.8
## - test_prep:practice_sport                2     223.8 62791 3113.8
## - parent_educ:parent_marital_status      13    2624.7 65192 3113.9
## - gender:is_first_child                   1      33.5 62600 3114.0
## - ethnic_group:lunch_type                 4     675.1 63242 3114.0
## - test_prep:is_first_child                1      43.5 62610 3114.1
## - practice_sport:is_first_child           2     284.8 62852 3114.4
## - lunch_type:parent_marital_status        2     286.8 62854 3114.4
## - test_prep:transport_means               1     107.4 62674 3114.7
## - parent_educ:practice_sport             10    2081.2 64648 3115.0
## - is_first_child:transport_means          1     173.0 62740 3115.3
## - lunch_type:is_first_child               1     198.5 62765 3115.6
## - parent_marital_status:transport_means   3     631.4 63198 3115.6
## <none>                                                62567 3115.7
## - lunch_type:transport_means              1     233.7 62801 3115.9
## - test_prep:wkly_study_hours              2     483.1 63050 3116.2
## - ethnic_group:is_first_child             4     945.3 63512 3116.5
## - practice_sport:transport_means          2     532.5 63099 3116.7
## - ethnic_group:transport_means            4     994.0 63561 3117.0
## - practice_sport:wkly_study_hours         4    1093.7 63661 3117.9
## - ethnic_group:parent_marital_status      9    2217.3 64784 3118.2
## - parent_educ:is_first_child              5    1371.0 63938 3118.5
## - lunch_type:wkly_study_hours             2     842.3 63409 3119.6
## - lunch_type:practice_sport               2    1121.1 63688 3122.2
## + ethnic_group:parent_educ               20    3285.4 59282 3123.9
## + parent_educ:test_prep                   5     169.0 62398 3124.1
## - parent_marital_status:wkly_study_hours  4    1981.5 64548 3126.1
## - parent_marital_status:is_first_child    2    2099.4 64666 3131.2
## 
## Step:  AIC=3107.54
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:wkly_study_hours           10   1414.74 64820 3100.6
## - gender:parent_marital_status            3     21.12 63426 3101.7
## - parent_marital_status:practice_sport    4    273.36 63679 3102.1
## - parent_educ:lunch_type                  5    538.08 63943 3102.5
## - ethnic_group:practice_sport             8   1242.25 64647 3103.0
## - parent_educ:transport_means             5    629.09 64034 3103.4
## - transport_means:wkly_study_hours        2     74.29 63480 3104.2
## - gender:ethnic_group                     4    521.25 63926 3104.4
## - ethnic_group:test_prep                  4    528.77 63934 3104.4
## - parent_educ:parent_marital_status      13   2521.02 65926 3104.5
## - gender:wkly_study_hours                 2    111.28 63517 3104.6
## - test_prep:parent_marital_status         2    160.78 63566 3105.0
## - gender:parent_educ                      5    835.10 64240 3105.3
## - gender:practice_sport                   2    198.93 63604 3105.4
## - is_first_child:wkly_study_hours         2    202.74 63608 3105.4
## - lunch_type:test_prep                    1      0.02 63405 3105.5
## - gender:transport_means                  1      1.41 63407 3105.6
## - test_prep:practice_sport                2    223.33 63629 3105.6
## - gender:lunch_type                       1      9.19 63414 3105.6
## - gender:test_prep                        1     10.73 63416 3105.6
## - gender:is_first_child                   1     19.04 63424 3105.7
## - lunch_type:parent_marital_status        2    263.90 63669 3106.0
## - test_prep:is_first_child                1     61.13 63466 3106.1
## - test_prep:transport_means               1     83.82 63489 3106.3
## - ethnic_group:lunch_type                 4    737.87 64143 3106.4
## - practice_sport:is_first_child           2    307.72 63713 3106.4
## - parent_educ:practice_sport             10   2084.34 65490 3106.6
## - is_first_child:transport_means          1    182.81 63588 3107.2
## - lunch_type:transport_means              1    190.55 63596 3107.3
## <none>                                                63405 3107.5
## - lunch_type:is_first_child               1    222.45 63628 3107.6
## - parent_marital_status:transport_means   3    668.96 64074 3107.7
## - ethnic_group:is_first_child             4    906.30 64312 3107.9
## - test_prep:wkly_study_hours              2    479.44 63885 3108.0
## - practice_sport:transport_means          2    522.81 63928 3108.4
## - ethnic_group:transport_means            4   1002.86 64408 3108.8
## - ethnic_group:parent_marital_status      9   2134.54 65540 3109.1
## - parent_educ:is_first_child              5   1308.56 64714 3109.6
## - practice_sport:wkly_study_hours         4   1141.24 64546 3110.1
## - lunch_type:wkly_study_hours             2    905.28 64311 3111.9
## - lunch_type:practice_sport               2   1150.67 64556 3114.2
## + ethnic_group:wkly_study_hours           8    838.30 62567 3115.7
## + parent_educ:test_prep                   5    193.76 63211 3115.7
## - parent_marital_status:wkly_study_hours  4   1837.59 65243 3116.4
## + ethnic_group:parent_educ               20   3031.37 60374 3118.6
## - parent_marital_status:is_first_child    2   1979.54 65385 3121.7
## 
## Step:  AIC=3100.56
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_marital_status            3      8.23 64828 3094.6
## - parent_educ:lunch_type                  5    450.88 65271 3094.7
## - ethnic_group:practice_sport             8   1175.09 65995 3095.2
## - parent_marital_status:practice_sport    4    329.09 65149 3095.5
## - parent_educ:transport_means             5    709.12 65529 3097.0
## - gender:ethnic_group                     4    488.42 65308 3097.0
## - ethnic_group:test_prep                  4    513.16 65333 3097.2
## - transport_means:wkly_study_hours        2    111.53 64932 3097.6
## - gender:parent_educ                      5    786.39 65606 3097.7
## - test_prep:parent_marital_status         2    128.82 64949 3097.7
## - is_first_child:wkly_study_hours         2    153.41 64973 3097.9
## - ethnic_group:lunch_type                 4    608.64 65429 3098.1
## - gender:practice_sport                   2    169.79 64990 3098.1
## - gender:transport_means                  1      0.57 64821 3098.6
## - lunch_type:test_prep                    1      2.61 64823 3098.6
## - gender:wkly_study_hours                 2    223.32 65043 3098.6
## - practice_sport:is_first_child           2    227.73 65048 3098.6
## - gender:lunch_type                       1      9.90 64830 3098.7
## - gender:test_prep                        1     17.01 64837 3098.7
## - gender:is_first_child                   1     29.46 64849 3098.8
## - test_prep:is_first_child                1     46.22 64866 3099.0
## - test_prep:practice_sport                2    284.13 65104 3099.1
## - lunch_type:parent_marital_status        2    297.47 65117 3099.3
## - test_prep:transport_means               1     90.44 64910 3099.4
## - parent_educ:parent_marital_status      13   2797.67 67618 3099.5
## - lunch_type:is_first_child               1    167.64 64988 3100.1
## - practice_sport:transport_means          2    388.54 65209 3100.1
## - is_first_child:transport_means          1    187.17 65007 3100.3
## <none>                                                64820 3100.6
## - ethnic_group:transport_means            4    890.45 65710 3100.6
## - practice_sport:wkly_study_hours         4    895.41 65715 3100.7
## - lunch_type:transport_means              1    231.07 65051 3100.7
## - parent_marital_status:transport_means   3    689.01 65509 3100.8
## - parent_educ:practice_sport             10   2285.42 67105 3101.0
## - ethnic_group:is_first_child             4    941.18 65761 3101.1
## - test_prep:wkly_study_hours              2    567.28 65387 3101.7
## - parent_educ:is_first_child              5   1260.35 66080 3101.9
## - lunch_type:wkly_study_hours             2    732.64 65553 3103.2
## - ethnic_group:parent_marital_status      9   2313.61 67134 3103.2
## - lunch_type:practice_sport               2   1122.55 65943 3106.7
## + parent_educ:wkly_study_hours           10   1414.74 63405 3107.5
## + ethnic_group:wkly_study_hours           8    942.30 63878 3107.9
## + parent_educ:test_prep                   5    254.90 64565 3108.2
## - parent_marital_status:wkly_study_hours  4   2025.70 66846 3110.7
## + ethnic_group:parent_educ               20   2750.70 62069 3115.0
## - parent_marital_status:is_first_child    2   2080.59 66901 3115.2
## 
## Step:  AIC=3094.63
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:lunch_type                  5    453.76 65282 3088.8
## - ethnic_group:practice_sport             8   1171.59 66000 3089.2
## - parent_marital_status:practice_sport    4    327.63 65156 3089.6
## - parent_educ:transport_means             5    704.99 65533 3091.0
## - gender:ethnic_group                     4    484.60 65313 3091.0
## - ethnic_group:test_prep                  4    518.12 65346 3091.3
## - transport_means:wkly_study_hours        2    112.25 64940 3091.7
## - test_prep:parent_marital_status         2    129.44 64958 3091.8
## - gender:parent_educ                      5    802.53 65631 3091.9
## - is_first_child:wkly_study_hours         2    150.98 64979 3092.0
## - ethnic_group:lunch_type                 4    611.63 65440 3092.2
## - gender:practice_sport                   2    175.34 65004 3092.2
## - gender:transport_means                  1      0.68 64829 3092.6
## - lunch_type:test_prep                    1      2.43 64831 3092.7
## - practice_sport:is_first_child           2    227.81 65056 3092.7
## - gender:lunch_type                       1      9.03 64837 3092.7
## - gender:wkly_study_hours                 2    232.70 65061 3092.7
## - gender:test_prep                        1     17.92 64846 3092.8
## - gender:is_first_child                   1     32.58 64861 3092.9
## - test_prep:is_first_child                1     46.46 64875 3093.1
## - test_prep:practice_sport                2    295.19 65123 3093.3
## - test_prep:transport_means               1     89.71 64918 3093.4
## - lunch_type:parent_marital_status        2    325.21 65153 3093.6
## - parent_educ:parent_marital_status      13   2846.27 67674 3094.0
## - practice_sport:transport_means          2    384.18 65212 3094.1
## - lunch_type:is_first_child               1    169.80 64998 3094.2
## - is_first_child:transport_means          1    197.72 65026 3094.4
## <none>                                                64828 3094.6
## - ethnic_group:transport_means            4    891.25 65719 3094.7
## - lunch_type:transport_means              1    237.39 65066 3094.8
## - practice_sport:wkly_study_hours         4    914.03 65742 3094.9
## - ethnic_group:is_first_child             4    941.88 65770 3095.1
## - parent_educ:practice_sport             10   2323.35 67152 3095.4
## - test_prep:wkly_study_hours              2    565.73 65394 3095.8
## - parent_marital_status:transport_means   3    799.54 65628 3095.9
## - parent_educ:is_first_child              5   1262.58 66091 3096.0
## - lunch_type:wkly_study_hours             2    745.49 65574 3097.4
## - ethnic_group:parent_marital_status      9   2441.41 67270 3098.4
## + gender:parent_marital_status            3      8.23 64820 3100.6
## - lunch_type:practice_sport               2   1165.09 65993 3101.1
## + parent_educ:wkly_study_hours           10   1401.85 63426 3101.7
## + ethnic_group:wkly_study_hours           8    943.83 63884 3102.0
## + parent_educ:test_prep                   5    256.20 64572 3102.3
## - parent_marital_status:wkly_study_hours  4   2029.22 66857 3104.8
## + ethnic_group:parent_educ               20   2749.68 62079 3109.1
## - parent_marital_status:is_first_child    2   2115.57 66944 3109.6
## 
## Step:  AIC=3088.75
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:practice_sport             8   1102.72 66385 3082.6
## - parent_marital_status:practice_sport    4    362.52 65644 3084.0
## - gender:ethnic_group                     4    473.96 65756 3085.0
## - parent_educ:transport_means             5    705.99 65988 3085.1
## - gender:parent_educ                      5    730.18 66012 3085.3
## - ethnic_group:test_prep                  4    552.03 65834 3085.7
## - test_prep:parent_marital_status         2    124.91 65407 3085.9
## - transport_means:wkly_study_hours        2    125.88 65408 3085.9
## - ethnic_group:lunch_type                 4    589.22 65871 3086.1
## - is_first_child:wkly_study_hours         2    147.84 65430 3086.1
## - gender:practice_sport                   2    177.50 65459 3086.3
## - gender:wkly_study_hours                 2    210.11 65492 3086.6
## - gender:transport_means                  1      0.48 65282 3086.8
## - lunch_type:test_prep                    1      3.83 65286 3086.8
## - gender:test_prep                        1     15.37 65297 3086.9
## - practice_sport:is_first_child           2    240.28 65522 3086.9
## - gender:lunch_type                       1     24.06 65306 3087.0
## - test_prep:is_first_child                1     34.65 65317 3087.1
## - gender:is_first_child                   1     64.33 65346 3087.3
## - lunch_type:parent_marital_status        2    294.12 65576 3087.4
## - test_prep:transport_means               1    113.55 65396 3087.8
## - test_prep:practice_sport                2    351.93 65634 3087.9
## - lunch_type:is_first_child               1    140.20 65422 3088.0
## - ethnic_group:transport_means            4    848.96 66131 3088.4
## - is_first_child:transport_means          1    183.22 65465 3088.4
## <none>                                                65282 3088.8
## - practice_sport:transport_means          2    445.89 65728 3088.8
## - parent_educ:parent_marital_status      13   2963.47 68245 3088.9
## - lunch_type:transport_means              1    274.34 65556 3089.2
## - ethnic_group:is_first_child             4    953.00 66235 3089.3
## - practice_sport:wkly_study_hours         4    967.93 66250 3089.4
## - parent_educ:practice_sport             10   2339.85 67622 3089.5
## - parent_educ:is_first_child              5   1226.98 66509 3089.7
## - test_prep:wkly_study_hours              2    569.64 65852 3089.9
## - parent_marital_status:transport_means   3    859.31 66141 3090.5
## - lunch_type:wkly_study_hours             2    714.94 65997 3091.2
## - ethnic_group:parent_marital_status      9   2385.39 67667 3091.9
## + parent_educ:lunch_type                  5    453.76 64828 3094.6
## + gender:parent_marital_status            3     11.11 65271 3094.7
## - lunch_type:practice_sport               2   1117.40 66399 3094.8
## + ethnic_group:wkly_study_hours           8    944.83 64337 3096.1
## + parent_educ:wkly_study_hours           10   1311.24 63971 3096.8
## + parent_educ:test_prep                   5    207.94 65074 3096.9
## - parent_marital_status:wkly_study_hours  4   2112.97 67395 3099.5
## + ethnic_group:parent_educ               20   2782.22 62500 3103.1
## - parent_marital_status:is_first_child    2   2274.32 67556 3104.9
## 
## Step:  AIC=3082.63
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:ethnic_group                     4    334.06 66719 3077.6
## - parent_educ:transport_means             5    602.59 66987 3078.0
## - gender:parent_educ                      5    667.19 67052 3078.5
## - parent_marital_status:practice_sport    4    536.65 66921 3079.4
## - ethnic_group:test_prep                  4    578.24 66963 3079.8
## - practice_sport:is_first_child           2    144.13 66529 3079.9
## - test_prep:parent_marital_status         2    152.27 66537 3080.0
## - transport_means:wkly_study_hours        2    160.57 66545 3080.1
## - is_first_child:wkly_study_hours         2    164.84 66550 3080.1
## - gender:transport_means                  1      1.29 66386 3080.6
## - gender:test_prep                        1      5.51 66390 3080.7
## - gender:lunch_type                       1     10.61 66395 3080.7
## - ethnic_group:lunch_type                 4    704.57 67089 3080.9
## - test_prep:is_first_child                1     28.20 66413 3080.9
## - gender:is_first_child                   1     30.57 66415 3080.9
## - lunch_type:test_prep                    1     31.63 66416 3080.9
## - test_prep:practice_sport                2    289.60 66674 3081.2
## - gender:wkly_study_hours                 2    292.89 66678 3081.2
## - lunch_type:parent_marital_status        2    313.74 66698 3081.4
## - parent_educ:parent_marital_status      13   2856.05 69241 3081.5
## - gender:practice_sport                   2    329.64 66714 3081.6
## - test_prep:transport_means               1    123.71 66508 3081.7
## - ethnic_group:is_first_child             4    851.65 67236 3082.2
## - ethnic_group:transport_means            4    854.21 67239 3082.2
## - lunch_type:is_first_child               1    178.29 66563 3082.2
## - practice_sport:transport_means          2    413.68 66798 3082.3
## - lunch_type:transport_means              1    210.36 66595 3082.5
## <none>                                                66385 3082.6
## - is_first_child:transport_means          1    226.07 66611 3082.6
## - test_prep:wkly_study_hours              2    457.36 66842 3082.7
## - practice_sport:wkly_study_hours         4    926.35 67311 3082.8
## - parent_educ:practice_sport             10   2400.56 68785 3083.6
## - parent_educ:is_first_child              5   1378.21 67763 3084.8
## - parent_marital_status:transport_means   3    938.11 67323 3084.9
## - lunch_type:wkly_study_hours             2    734.78 67119 3085.1
## - ethnic_group:parent_marital_status      9   2431.75 68816 3085.8
## - lunch_type:practice_sport               2   1041.78 67426 3087.8
## + gender:parent_marital_status            3      8.49 66376 3088.6
## + ethnic_group:practice_sport             8   1102.72 65282 3088.8
## + parent_educ:lunch_type                  5    384.89 66000 3089.2
## + ethnic_group:wkly_study_hours           8    970.65 65414 3089.9
## + parent_educ:test_prep                   5    200.85 66184 3090.8
## + parent_educ:wkly_study_hours           10   1239.53 65145 3091.5
## - parent_marital_status:wkly_study_hours  4   2251.07 68636 3094.3
## - parent_marital_status:is_first_child    2   2096.19 68481 3097.0
## + ethnic_group:parent_educ               20   2346.89 64038 3101.4
## 
## Step:  AIC=3077.59
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:parent_educ + 
##     gender:lunch_type + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:transport_means             5    543.87 67263 3072.4
## - gender:parent_educ                      5    573.95 67293 3072.6
## - ethnic_group:test_prep                  4    502.89 67222 3074.0
## - parent_marital_status:practice_sport    4    539.12 67258 3074.3
## - test_prep:parent_marital_status         2    143.84 66863 3074.9
## - is_first_child:wkly_study_hours         2    166.05 66885 3075.1
## - practice_sport:is_first_child           2    168.91 66888 3075.1
## - transport_means:wkly_study_hours        2    184.33 66903 3075.2
## - gender:transport_means                  1      0.05 66719 3075.6
## - gender:test_prep                        1      4.59 66723 3075.6
## - gender:lunch_type                       1      8.88 66728 3075.7
## - ethnic_group:lunch_type                 4    701.29 67420 3075.8
## - test_prep:is_first_child                1     27.50 66746 3075.8
## - gender:is_first_child                   1     37.57 66756 3075.9
## - lunch_type:test_prep                    1     42.48 66761 3076.0
## - test_prep:practice_sport                2    284.58 67003 3076.1
## - lunch_type:parent_marital_status        2    300.95 67020 3076.2
## - gender:practice_sport                   2    316.56 67035 3076.4
## - gender:wkly_study_hours                 2    323.72 67042 3076.4
## - test_prep:transport_means               1    136.37 66855 3076.8
## - parent_educ:parent_marital_status      13   2927.80 69647 3076.9
## - ethnic_group:is_first_child             4    837.49 67556 3076.9
## - ethnic_group:transport_means            4    843.50 67562 3077.0
## - practice_sport:transport_means          2    404.91 67124 3077.2
## - lunch_type:is_first_child               1    185.14 66904 3077.2
## - lunch_type:transport_means              1    215.15 66934 3077.5
## <none>                                                66719 3077.6
## - is_first_child:transport_means          1    247.01 66966 3077.8
## - test_prep:wkly_study_hours              2    499.70 67218 3078.0
## - practice_sport:wkly_study_hours         4    963.49 67682 3078.1
## - parent_educ:practice_sport             10   2429.40 69148 3078.7
## - ethnic_group:parent_marital_status      9   2321.43 69040 3079.8
## - parent_marital_status:transport_means   3    952.44 67671 3079.9
## - lunch_type:wkly_study_hours             2    735.88 67455 3080.1
## - parent_educ:is_first_child              5   1473.91 68193 3080.5
## + gender:ethnic_group                     4    334.06 66385 3082.6
## + gender:parent_marital_status            3      9.39 66709 3083.5
## - lunch_type:practice_sport               2   1175.07 67894 3083.9
## + parent_educ:lunch_type                  5    385.08 66334 3084.2
## + ethnic_group:wkly_study_hours           8    973.05 65746 3084.9
## + ethnic_group:practice_sport             8    962.81 65756 3085.0
## + parent_educ:test_prep                   5    159.07 66560 3086.2
## + parent_educ:wkly_study_hours           10   1225.64 65493 3086.7
## - parent_marital_status:wkly_study_hours  4   2289.79 69009 3089.5
## - parent_marital_status:is_first_child    2   2193.29 68912 3092.7
## + ethnic_group:parent_educ               20   2280.02 64439 3097.1
## 
## Step:  AIC=3072.38
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:parent_educ + 
##     gender:lunch_type + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_educ                      5    579.12 67842 3067.4
## - ethnic_group:test_prep                  4    537.48 67800 3069.1
## - parent_marital_status:practice_sport    4    539.25 67802 3069.1
## - test_prep:parent_marital_status         2    134.95 67398 3069.6
## - practice_sport:is_first_child           2    135.32 67398 3069.6
## - is_first_child:wkly_study_hours         2    153.61 67416 3069.7
## - transport_means:wkly_study_hours        2    184.05 67447 3070.0
## - gender:transport_means                  1      0.09 67263 3070.4
## - gender:test_prep                        1      1.81 67264 3070.4
## - gender:lunch_type                       1     15.08 67278 3070.5
## - gender:is_first_child                   1     33.95 67297 3070.7
## - gender:wkly_study_hours                 2    266.92 67530 3070.7
## - test_prep:is_first_child                1     50.08 67313 3070.8
## - lunch_type:test_prep                    1     58.79 67321 3070.9
## - test_prep:practice_sport                2    301.02 67564 3071.0
## - ethnic_group:lunch_type                 4    765.58 68028 3071.1
## - practice_sport:transport_means          2    331.21 67594 3071.3
## - parent_educ:parent_marital_status      13   2920.47 70183 3071.5
## - gender:practice_sport                   2    354.13 67617 3071.5
## - lunch_type:parent_marital_status        2    356.61 67619 3071.5
## - test_prep:transport_means               1    161.49 67424 3071.8
## - ethnic_group:is_first_child             4    860.27 68123 3071.9
## - lunch_type:is_first_child               1    192.18 67455 3072.1
## - is_first_child:transport_means          1    210.90 67474 3072.2
## - lunch_type:transport_means              1    213.26 67476 3072.2
## <none>                                                67263 3072.4
## - ethnic_group:transport_means            4    960.94 68224 3072.8
## - test_prep:wkly_study_hours              2    521.24 67784 3072.9
## - parent_educ:practice_sport             10   2393.16 69656 3073.0
## - practice_sport:wkly_study_hours         4   1070.29 68333 3073.7
## - parent_marital_status:transport_means   3    845.76 68108 3073.8
## - parent_educ:is_first_child              5   1453.38 68716 3075.0
## - ethnic_group:parent_marital_status      9   2419.49 69682 3075.2
## - lunch_type:wkly_study_hours             2    855.76 68118 3075.8
## + parent_educ:transport_means             5    543.87 66719 3077.6
## + gender:ethnic_group                     4    275.34 66987 3078.0
## + gender:parent_marital_status            3     15.46 67247 3078.2
## + parent_educ:lunch_type                  5    384.38 66878 3079.0
## - lunch_type:practice_sport               2   1273.57 68536 3079.4
## + ethnic_group:wkly_study_hours           8    916.36 66346 3080.3
## + parent_educ:test_prep                   5    205.37 67057 3080.6
## + ethnic_group:practice_sport             8    878.28 66384 3080.6
## + parent_educ:wkly_study_hours           10   1247.47 66015 3081.3
## - parent_marital_status:wkly_study_hours  4   2322.31 69585 3084.4
## - parent_marital_status:is_first_child    2   2177.48 69440 3087.2
## + ethnic_group:parent_educ               20   2463.59 64799 3090.4
## 
## Step:  AIC=3067.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:test_prep                  4     472.9 68315 3063.5
## - parent_marital_status:practice_sport    4     538.6 68380 3064.1
## - test_prep:parent_marital_status         2     116.3 67958 3064.4
## - practice_sport:is_first_child           2     164.3 68006 3064.9
## - is_first_child:wkly_study_hours         2     175.1 68017 3065.0
## - transport_means:wkly_study_hours        2     188.2 68030 3065.1
## - gender:transport_means                  1       0.1 67842 3065.4
## - gender:test_prep                        1       1.5 67843 3065.4
## - ethnic_group:lunch_type                 4     700.2 68542 3065.5
## - gender:lunch_type                       1      16.1 67858 3065.6
## - gender:is_first_child                   1      34.3 67876 3065.7
## - gender:wkly_study_hours                 2     295.8 68138 3066.0
## - practice_sport:transport_means          2     303.3 68145 3066.1
## - test_prep:is_first_child                1      73.1 67915 3066.1
## - lunch_type:test_prep                    1      80.4 67922 3066.1
## - lunch_type:parent_marital_status        2     345.7 68187 3066.4
## - test_prep:practice_sport                2     352.4 68194 3066.5
## - gender:practice_sport                   2     362.5 68204 3066.6
## - test_prep:transport_means               1     158.6 68000 3066.8
## - ethnic_group:is_first_child             4     855.9 68698 3066.8
## - is_first_child:transport_means          1     195.1 68037 3067.1
## - lunch_type:is_first_child               1     204.2 68046 3067.2
## <none>                                                67842 3067.4
## - parent_educ:practice_sport             10    2394.3 70236 3067.9
## - lunch_type:transport_means              1     288.9 68131 3067.9
## - test_prep:wkly_study_hours              2     576.3 68418 3068.4
## - practice_sport:wkly_study_hours         4    1062.6 68904 3068.6
## - parent_educ:is_first_child              5    1333.5 69175 3068.9
## - parent_educ:parent_marital_status      13    3262.6 71104 3069.2
## - ethnic_group:transport_means            4    1140.1 68982 3069.3
## - parent_marital_status:transport_means   3     926.1 68768 3069.4
## - ethnic_group:parent_marital_status      9    2363.8 70206 3069.7
## - lunch_type:wkly_study_hours             2     879.5 68721 3071.0
## + gender:parent_educ                      5     579.1 67263 3072.4
## + parent_educ:transport_means             5     549.0 67293 3072.6
## + gender:parent_marital_status            3       4.7 67837 3073.4
## + gender:ethnic_group                     4     194.0 67648 3073.8
## + parent_educ:lunch_type                  5     343.0 67499 3074.4
## - lunch_type:practice_sport               2    1328.3 69170 3074.9
## + ethnic_group:wkly_study_hours           8     895.6 66946 3075.6
## + parent_educ:test_prep                   5     172.0 67670 3075.9
## + ethnic_group:practice_sport             8     845.9 66996 3076.0
## + parent_educ:wkly_study_hours           10    1223.0 66619 3076.7
## - parent_marital_status:wkly_study_hours  4    2407.9 70250 3080.0
## - parent_marital_status:is_first_child    2    2111.7 69953 3081.5
## + ethnic_group:parent_educ               20    2467.1 65375 3085.6
## 
## Step:  AIC=3063.54
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:practice_sport    4     515.8 68830 3060.0
## - test_prep:parent_marital_status         2     135.4 68450 3060.7
## - ethnic_group:lunch_type                 4     622.0 68937 3060.9
## - is_first_child:wkly_study_hours         2     165.2 68480 3061.0
## - transport_means:wkly_study_hours        2     186.3 68501 3061.1
## - practice_sport:is_first_child           2     200.7 68515 3061.3
## - gender:test_prep                        1       0.1 68315 3061.5
## - gender:transport_means                  1       0.1 68315 3061.5
## - gender:lunch_type                       1       9.7 68324 3061.6
## - gender:is_first_child                   1      17.5 68332 3061.7
## - test_prep:practice_sport                2     287.2 68602 3062.0
## - test_prep:is_first_child                1      69.2 68384 3062.1
## - gender:wkly_study_hours                 2     303.9 68619 3062.2
## - practice_sport:transport_means          2     316.7 68631 3062.3
## - lunch_type:test_prep                    1     103.0 68418 3062.4
## - gender:practice_sport                   2     362.7 68677 3062.7
## - lunch_type:parent_marital_status        2     373.3 68688 3062.8
## - ethnic_group:is_first_child             4     849.9 69165 3062.8
## - test_prep:transport_means               1     196.2 68511 3063.2
## - is_first_child:transport_means          1     200.9 68515 3063.3
## - lunch_type:is_first_child               1     207.4 68522 3063.3
## <none>                                                68315 3063.5
## - parent_educ:practice_sport             10    2386.3 70701 3063.8
## - lunch_type:transport_means              1     325.6 68640 3064.3
## - practice_sport:wkly_study_hours         4    1079.2 69394 3064.8
## - parent_educ:is_first_child              5    1328.6 69643 3064.9
## - test_prep:wkly_study_hours              2     642.6 68957 3065.1
## - parent_educ:parent_marital_status      13    3270.8 71585 3065.1
## - parent_marital_status:transport_means   3     893.5 69208 3065.2
## - ethnic_group:parent_marital_status      9    2398.8 70713 3065.9
## - ethnic_group:transport_means            4    1216.2 69531 3065.9
## - lunch_type:wkly_study_hours             2     883.9 69199 3067.1
## + ethnic_group:test_prep                  4     472.9 67842 3067.4
## + parent_educ:transport_means             5     580.8 67734 3068.5
## + gender:parent_educ                      5     514.5 67800 3069.1
## + gender:parent_marital_status            3       4.7 68310 3069.5
## + gender:ethnic_group                     4     157.4 68157 3070.2
## + parent_educ:lunch_type                  5     352.3 67962 3070.5
## + ethnic_group:wkly_study_hours           8     891.3 67423 3071.8
## - lunch_type:practice_sport               2    1447.4 69762 3071.9
## + ethnic_group:practice_sport             8     870.0 67445 3072.0
## + parent_educ:wkly_study_hours           10    1235.0 67080 3072.8
## + parent_educ:test_prep                   5      87.1 68228 3072.8
## - parent_marital_status:wkly_study_hours  4    2256.3 70571 3074.7
## - parent_marital_status:is_first_child    2    2108.8 70423 3077.5
## + ethnic_group:parent_educ               20    2467.3 65847 3081.8
## 
## Step:  AIC=3059.97
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:parent_marital_status         2     118.5 68949 3057.0
## - practice_sport:is_first_child           2     135.1 68966 3057.1
## - lunch_type:parent_marital_status        3     380.8 69211 3057.2
## - transport_means:wkly_study_hours        2     180.1 69011 3057.5
## - is_first_child:wkly_study_hours         2     208.2 69039 3057.8
## - ethnic_group:lunch_type                 4     693.2 69524 3057.9
## - gender:transport_means                  1       0.1 68831 3058.0
## - gender:test_prep                        1       1.6 68832 3058.0
## - gender:is_first_child                   1      10.6 68841 3058.1
## - gender:lunch_type                       1      11.7 68842 3058.1
## - practice_sport:transport_means          2     277.5 69108 3058.3
## - test_prep:practice_sport                2     288.4 69119 3058.4
## - test_prep:is_first_child                1      63.3 68894 3058.5
## - gender:wkly_study_hours                 2     335.4 69166 3058.8
## - lunch_type:test_prep                    1     108.8 68939 3058.9
## - lunch_type:is_first_child               1     147.8 68978 3059.2
## - ethnic_group:is_first_child             4     868.0 69698 3059.4
## - gender:practice_sport                   2     400.2 69231 3059.4
## - test_prep:transport_means               1     173.0 69003 3059.5
## - parent_educ:practice_sport             10    2335.4 71166 3059.7
## - is_first_child:transport_means          1     222.7 69053 3059.9
## <none>                                                68830 3060.0
## - lunch_type:transport_means              1     270.9 69101 3060.3
## - ethnic_group:parent_marital_status     10    2412.2 71243 3060.3
## - parent_educ:is_first_child              5    1324.6 70155 3061.2
## - practice_sport:wkly_study_hours         4    1108.8 69939 3061.4
## - parent_marital_status:transport_means   3     877.4 69708 3061.4
## - ethnic_group:transport_means            4    1123.2 69954 3061.5
## - test_prep:wkly_study_hours              2     713.3 69544 3062.1
## - parent_educ:parent_marital_status      14    3646.4 72477 3062.4
## - lunch_type:wkly_study_hours             2     867.7 69698 3063.4
## + parent_marital_status:practice_sport    4     515.8 68315 3063.5
## + ethnic_group:test_prep                  4     450.1 68380 3064.1
## + parent_educ:transport_means             5     597.6 68233 3064.8
## + gender:parent_educ                      5     512.3 68318 3065.6
## + gender:parent_marital_status            3       3.7 68827 3065.9
## + gender:ethnic_group                     4     171.0 68659 3066.5
## + parent_educ:lunch_type                  5     376.4 68454 3066.7
## + ethnic_group:practice_sport             8     991.3 67839 3067.4
## - lunch_type:practice_sport               2    1394.4 70225 3067.8
## + parent_educ:wkly_study_hours           10    1326.5 67504 3068.5
## + parent_educ:test_prep                   5      91.2 68739 3069.2
## + ethnic_group:wkly_study_hours           8     764.8 68066 3069.4
## - parent_marital_status:wkly_study_hours  5    2336.3 71167 3069.7
## - parent_marital_status:is_first_child    2    2343.8 71174 3075.7
## + ethnic_group:parent_educ               20    2528.6 66302 3077.9
## 
## Step:  AIC=3056.99
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:parent_marital_status        3     363.1 69312 3054.1
## - practice_sport:is_first_child           2     128.7 69078 3054.1
## - transport_means:wkly_study_hours        2     187.6 69137 3054.6
## - is_first_child:wkly_study_hours         2     219.9 69169 3054.9
## - gender:transport_means                  1       0.0 68949 3055.0
## - gender:test_prep                        1       0.9 68950 3055.0
## - ethnic_group:lunch_type                 4     708.8 69658 3055.0
## - gender:is_first_child                   1      12.3 68961 3055.1
## - gender:lunch_type                       1      13.4 68962 3055.1
## - practice_sport:transport_means          2     279.0 69228 3055.4
## - test_prep:practice_sport                2     309.6 69259 3055.6
## - test_prep:is_first_child                1      81.0 69030 3055.7
## - gender:wkly_study_hours                 2     339.7 69289 3055.9
## - ethnic_group:parent_marital_status     11    2493.0 71442 3055.9
## - lunch_type:test_prep                    1     116.7 69066 3056.0
## - lunch_type:is_first_child               1     130.3 69079 3056.1
## - gender:practice_sport                   2     390.2 69339 3056.3
## - test_prep:transport_means               1     190.2 69139 3056.6
## - parent_educ:practice_sport             10    2364.1 71313 3056.9
## - is_first_child:transport_means          1     221.4 69170 3056.9
## <none>                                                68949 3057.0
## - ethnic_group:is_first_child             4     941.5 69890 3057.0
## - lunch_type:transport_means              1     271.5 69221 3057.3
## - practice_sport:wkly_study_hours         4    1068.4 70017 3058.1
## - parent_educ:parent_marital_status      15    3736.4 72685 3058.1
## - parent_educ:is_first_child              5    1326.1 70275 3058.2
## - ethnic_group:transport_means            4    1133.8 70083 3058.6
## - parent_marital_status:transport_means   3     949.4 69898 3059.1
## - test_prep:wkly_study_hours              2     717.9 69667 3059.1
## + test_prep:parent_marital_status         2     118.5 68830 3060.0
## - lunch_type:wkly_study_hours             2     854.3 69803 3060.3
## + parent_marital_status:practice_sport    4     498.9 68450 3060.7
## + ethnic_group:test_prep                  4     471.9 68477 3060.9
## + parent_educ:transport_means             5     594.1 68355 3061.9
## + gender:parent_educ                      5     487.7 68461 3062.8
## + gender:parent_marital_status            3       3.2 68946 3063.0
## + gender:ethnic_group                     4     173.1 68776 3063.5
## + parent_educ:lunch_type                  5     381.0 68568 3063.7
## + ethnic_group:practice_sport             8    1010.9 67938 3064.3
## - lunch_type:practice_sport               2    1364.2 70313 3064.6
## + parent_educ:wkly_study_hours           10    1310.2 67639 3065.7
## + ethnic_group:wkly_study_hours           8     808.1 68141 3066.0
## + parent_educ:test_prep                   5      83.1 68866 3066.3
## - parent_marital_status:wkly_study_hours  6    2636.8 71586 3067.1
## - parent_marital_status:is_first_child    3    2492.4 71441 3071.9
## + ethnic_group:parent_educ               20    2530.7 66418 3074.9
## 
## Step:  AIC=3054.09
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:is_first_child           2     102.1 69414 3051.0
## - is_first_child:wkly_study_hours         2     207.0 69519 3051.8
## - ethnic_group:parent_marital_status     11    2366.0 71678 3051.9
## - transport_means:wkly_study_hours        2     212.7 69525 3051.9
## - gender:transport_means                  1       1.3 69313 3052.1
## - gender:test_prep                        1       3.7 69316 3052.1
## - ethnic_group:lunch_type                 4     722.5 70035 3052.2
## - gender:is_first_child                   1      19.3 69331 3052.2
## - gender:lunch_type                       1      29.1 69341 3052.3
## - practice_sport:transport_means          2     265.1 69577 3052.3
## - gender:wkly_study_hours                 2     288.0 69600 3052.5
## - test_prep:is_first_child                1      76.6 69389 3052.7
## - test_prep:practice_sport                2     327.5 69640 3052.9
## - gender:practice_sport                   2     339.9 69652 3053.0
## - lunch_type:test_prep                    1     110.6 69423 3053.0
## - lunch_type:is_first_child               1     118.9 69431 3053.1
## - parent_educ:practice_sport             10    2314.2 71626 3053.5
## - ethnic_group:is_first_child             4     882.6 70195 3053.6
## - test_prep:transport_means               1     191.4 69503 3053.7
## <none>                                                69312 3054.1
## - is_first_child:transport_means          1     236.1 69548 3054.1
## - lunch_type:transport_means              1     283.0 69595 3054.5
## - practice_sport:wkly_study_hours         4    1043.8 70356 3054.9
## - parent_educ:is_first_child              5    1292.5 70605 3055.0
## - ethnic_group:transport_means            4    1109.2 70421 3055.5
## - parent_educ:parent_marital_status      15    3835.0 73147 3055.9
## - parent_marital_status:transport_means   3     935.7 70248 3056.0
## - test_prep:wkly_study_hours              2     703.5 70016 3056.1
## - lunch_type:wkly_study_hours             2     778.6 70091 3056.7
## + lunch_type:parent_marital_status        3     363.1 68949 3057.0
## + test_prep:parent_marital_status         2     100.8 69211 3057.2
## + ethnic_group:test_prep                  4     502.5 68810 3057.8
## + parent_educ:transport_means             5     651.6 68660 3058.5
## + parent_marital_status:practice_sport    5     507.8 68804 3059.8
## + gender:parent_marital_status            3      19.6 69293 3059.9
## + gender:parent_educ                      5     471.7 68840 3060.1
## + gender:ethnic_group                     4     167.2 69145 3060.7
## - lunch_type:practice_sport               2    1267.6 70580 3060.8
## + parent_educ:lunch_type                  5     356.7 68955 3061.0
## + ethnic_group:practice_sport             8    1016.1 68296 3061.4
## + parent_educ:wkly_study_hours           10    1340.9 67971 3062.6
## + ethnic_group:wkly_study_hours           8     789.2 68523 3063.3
## - parent_marital_status:wkly_study_hours  6    2550.9 71863 3063.4
## + parent_educ:test_prep                   5      50.5 69262 3063.7
## - parent_marital_status:is_first_child    3    2435.5 71748 3068.5
## + ethnic_group:parent_educ               20    2270.2 67042 3074.4
## 
## Step:  AIC=3050.96
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_marital_status     11    2305.2 71719 3048.2
## - is_first_child:wkly_study_hours         2     191.9 69606 3048.6
## - transport_means:wkly_study_hours        2     205.6 69620 3048.7
## - practice_sport:transport_means          2     236.5 69651 3049.0
## - gender:transport_means                  1       2.8 69417 3049.0
## - gender:test_prep                        1       5.6 69420 3049.0
## - ethnic_group:lunch_type                 4     724.5 70139 3049.1
## - gender:is_first_child                   1      23.6 69438 3049.2
## - gender:lunch_type                       1      38.5 69453 3049.3
## - test_prep:is_first_child                1      52.7 69467 3049.4
## - gender:wkly_study_hours                 2     289.2 69703 3049.4
## - gender:practice_sport                   2     343.5 69758 3049.9
## - test_prep:practice_sport                2     349.8 69764 3049.9
## - parent_educ:practice_sport             10    2272.3 71686 3050.0
## - lunch_type:test_prep                    1     128.0 69542 3050.0
## - lunch_type:is_first_child               1     131.7 69546 3050.1
## - test_prep:transport_means               1     191.5 69606 3050.6
## - ethnic_group:is_first_child             4     907.0 70321 3050.6
## <none>                                                69414 3051.0
## - lunch_type:transport_means              1     270.0 69684 3051.2
## - is_first_child:transport_means          1     271.7 69686 3051.3
## - parent_educ:is_first_child              5    1261.5 70676 3051.6
## - ethnic_group:transport_means            4    1065.9 70480 3051.9
## - practice_sport:wkly_study_hours         4    1075.9 70490 3052.0
## - parent_educ:parent_marital_status      15    3782.3 73197 3052.3
## - parent_marital_status:transport_means   3     901.5 70316 3052.6
## - test_prep:wkly_study_hours              2     673.0 70087 3052.7
## - lunch_type:wkly_study_hours             2     782.5 70197 3053.6
## + practice_sport:is_first_child           2     102.1 69312 3054.1
## + lunch_type:parent_marital_status        3     336.6 69078 3054.1
## + test_prep:parent_marital_status         2      97.8 69316 3054.1
## + ethnic_group:test_prep                  4     524.0 68890 3054.5
## + parent_educ:transport_means             5     604.0 68810 3055.8
## + gender:parent_marital_status            3      18.0 69396 3056.8
## + gender:parent_educ                      5     484.2 68930 3056.8
## + parent_marital_status:practice_sport    5     446.7 68968 3057.2
## - lunch_type:practice_sport               2    1235.0 70649 3057.4
## + gender:ethnic_group                     4     187.0 69227 3057.4
## + parent_educ:lunch_type                  5     356.3 69058 3057.9
## + ethnic_group:practice_sport             8     949.0 68465 3058.8
## + parent_educ:wkly_study_hours           10    1293.2 68121 3059.9
## + ethnic_group:wkly_study_hours           8     799.5 68615 3060.1
## - parent_marital_status:wkly_study_hours  6    2548.9 71963 3060.2
## + parent_educ:test_prep                   5      54.2 69360 3060.5
## - parent_marital_status:is_first_child    3    2469.3 71884 3065.6
## + ethnic_group:parent_educ               20    2240.2 67174 3071.6
## 
## Step:  AIC=3048.23
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:practice_sport             10    1945.7 73665 3044.0
## - practice_sport:transport_means          2      95.5 71815 3045.0
## - ethnic_group:is_first_child             4     586.8 72306 3045.0
## - transport_means:wkly_study_hours        2     160.4 71880 3045.6
## - is_first_child:wkly_study_hours         2     167.1 71886 3045.6
## - gender:wkly_study_hours                 2     199.5 71919 3045.9
## - ethnic_group:lunch_type                 4     741.3 72461 3046.3
## - gender:transport_means                  1      24.5 71744 3046.4
## - gender:test_prep                        1      37.7 71757 3046.5
## - test_prep:is_first_child                1      40.0 71759 3046.6
## - gender:lunch_type                       1      42.6 71762 3046.6
## - gender:is_first_child                   1      52.0 71771 3046.7
## - test_prep:practice_sport                2     296.9 72016 3046.7
## - gender:practice_sport                   2     338.7 72058 3047.0
## - lunch_type:test_prep                    1      98.2 71818 3047.0
## - lunch_type:is_first_child               1      98.2 71818 3047.0
## - test_prep:transport_means               1     173.5 71893 3047.7
## - parent_educ:is_first_child              5    1201.7 72921 3048.0
## <none>                                                71719 3048.2
## - parent_marital_status:transport_means   3     741.3 72461 3048.3
## - practice_sport:wkly_study_hours         4     990.2 72710 3048.3
## - lunch_type:transport_means              1     320.0 72039 3048.9
## - is_first_child:transport_means          1     356.3 72076 3049.2
## - ethnic_group:transport_means            4    1128.0 72847 3049.4
## - lunch_type:wkly_study_hours             2     705.8 72425 3050.0
## - parent_educ:parent_marital_status      15    3998.6 75718 3050.2
## - test_prep:wkly_study_hours              2     820.6 72540 3050.9
## + ethnic_group:parent_marital_status     11    2305.2 69414 3051.0
## + ethnic_group:test_prep                  4     586.9 71132 3051.4
## + practice_sport:is_first_child           2      41.3 71678 3051.9
## - parent_marital_status:wkly_study_hours  6    1941.0 73660 3052.0
## + parent_educ:transport_means             5     747.1 70972 3052.1
## + lunch_type:parent_marital_status        3     219.1 71500 3052.4
## + test_prep:parent_marital_status         3     147.7 71572 3053.0
## + gender:parent_marital_status            3      84.7 71635 3053.5
## + gender:parent_educ                      5     442.4 71277 3054.6
## - lunch_type:practice_sport               2    1319.4 73039 3055.0
## + gender:ethnic_group                     4     146.6 71573 3055.0
## + parent_educ:lunch_type                  5     373.5 71346 3055.2
## + parent_marital_status:practice_sport    6     525.2 71194 3055.9
## + parent_educ:wkly_study_hours           10    1465.5 70254 3056.1
## + ethnic_group:practice_sport             8     879.1 70840 3057.0
## + parent_educ:test_prep                   5      50.8 71669 3057.8
## + ethnic_group:wkly_study_hours           8     747.7 70972 3058.1
## - parent_marital_status:is_first_child    3    2272.4 73992 3060.6
## + ethnic_group:parent_educ               20    2384.6 69335 3068.3
## 
## Step:  AIC=3044.03
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:is_first_child             4     616.0 74281 3040.9
## - practice_sport:transport_means          2     114.9 73780 3040.9
## - transport_means:wkly_study_hours        2     119.6 73785 3041.0
## - is_first_child:wkly_study_hours         2     175.7 73841 3041.4
## - ethnic_group:lunch_type                 4     736.1 74401 3041.9
## - gender:wkly_study_hours                 2     246.2 73911 3042.0
## - gender:lunch_type                       1      26.0 73691 3042.2
## - gender:practice_sport                   2     279.5 73945 3042.3
## - test_prep:is_first_child                1      51.2 73716 3042.4
## - gender:transport_means                  1      53.1 73718 3042.4
## - gender:test_prep                        1      56.7 73722 3042.5
## - gender:is_first_child                   1      66.4 73731 3042.6
## - lunch_type:is_first_child               1      79.2 73744 3042.7
## - test_prep:practice_sport                2     349.4 74014 3042.8
## - lunch_type:test_prep                    1     121.2 73786 3043.0
## - practice_sport:wkly_study_hours         4     879.5 74545 3043.0
## - test_prep:transport_means               1     145.6 73811 3043.2
## <none>                                                73665 3044.0
## - is_first_child:transport_means          1     260.1 73925 3044.1
## - lunch_type:transport_means              1     285.2 73950 3044.3
## - parent_educ:is_first_child              5    1425.4 75090 3045.3
## - ethnic_group:transport_means            4    1173.7 74839 3045.3
## - test_prep:wkly_study_hours              2     674.2 74339 3045.4
## - parent_marital_status:transport_means   3     930.7 74596 3045.4
## - lunch_type:wkly_study_hours             2     751.1 74416 3046.0
## + ethnic_group:test_prep                  4     596.7 73068 3047.2
## + practice_sport:is_first_child           2      23.4 73642 3047.8
## - parent_educ:parent_marital_status      15    4352.1 78017 3047.9
## - parent_marital_status:wkly_study_hours  6    2020.8 75686 3048.0
## + parent_educ:practice_sport             10    1945.7 71719 3048.2
## + lunch_type:parent_marital_status        3     173.9 73491 3048.6
## + test_prep:parent_marital_status         3     155.5 73510 3048.8
## - lunch_type:practice_sport               2    1103.6 74769 3048.8
## + parent_educ:transport_means             5     643.4 73022 3048.8
## + gender:parent_marital_status            3      77.3 73588 3049.4
## + ethnic_group:parent_marital_status     11    1978.6 71686 3050.0
## + gender:ethnic_group                     4     239.4 73426 3050.1
## + gender:parent_educ                      5     474.1 73191 3050.2
## + parent_educ:wkly_study_hours           10    1601.0 72064 3051.1
## + parent_educ:lunch_type                  5     343.0 73322 3051.3
## + parent_marital_status:practice_sport    6     420.8 73244 3052.6
## + ethnic_group:practice_sport             8     895.6 72769 3052.8
## + parent_educ:test_prep                   5      96.6 73568 3053.2
## + ethnic_group:wkly_study_hours           8     768.5 72897 3053.8
## - parent_marital_status:is_first_child    3    2307.1 75972 3056.2
## + ethnic_group:parent_educ               20    2365.9 71299 3064.8
## 
## Step:  AIC=3040.94
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:lunch_type                 4     559.7 74841 3037.4
## - practice_sport:transport_means          2     104.8 74386 3037.8
## - transport_means:wkly_study_hours        2     126.4 74407 3037.9
## - gender:wkly_study_hours                 2     196.4 74477 3038.5
## - is_first_child:wkly_study_hours         2     229.6 74511 3038.8
## - gender:practice_sport                   2     251.9 74533 3038.9
## - gender:lunch_type                       1      14.3 74295 3039.1
## - gender:is_first_child                   1      30.8 74312 3039.2
## - gender:test_prep                        1      40.0 74321 3039.3
## - gender:transport_means                  1      58.5 74340 3039.4
## - test_prep:is_first_child                1      75.8 74357 3039.5
## - test_prep:practice_sport                2     350.0 74631 3039.7
## - test_prep:transport_means               1     115.1 74396 3039.8
## - lunch_type:is_first_child               1     119.2 74400 3039.9
## - practice_sport:wkly_study_hours         4     880.0 75161 3039.9
## - is_first_child:transport_means          1     144.6 74426 3040.1
## - lunch_type:test_prep                    1     149.4 74430 3040.1
## <none>                                                74281 3040.9
## - lunch_type:transport_means              1     261.8 74543 3041.0
## - test_prep:wkly_study_hours              2     522.3 74803 3041.1
## - parent_marital_status:transport_means   3     939.6 75221 3042.3
## - lunch_type:wkly_study_hours             2     692.9 74974 3042.4
## - parent_educ:is_first_child              5    1465.0 75746 3042.5
## - ethnic_group:transport_means            4    1307.4 75588 3043.2
## - parent_educ:parent_marital_status      15    4239.6 78521 3043.7
## + ethnic_group:is_first_child             4     616.0 73665 3044.0
## + ethnic_group:test_prep                  4     581.5 73700 3044.3
## - parent_marital_status:wkly_study_hours  6    1978.0 76259 3044.4
## + practice_sport:is_first_child           2      40.8 74240 3044.6
## + parent_educ:practice_sport             10    1974.9 72306 3045.0
## + test_prep:parent_marital_status         3     184.2 74097 3045.5
## - lunch_type:practice_sport               2    1103.4 75384 3045.6
## + lunch_type:parent_marital_status        3     140.1 74141 3045.8
## + parent_educ:transport_means             5     610.0 73671 3046.1
## + gender:parent_marital_status            3      67.0 74214 3046.4
## + gender:ethnic_group                     4     192.3 74089 3047.4
## + gender:parent_educ                      5     422.0 73859 3047.6
## + parent_educ:wkly_study_hours           10    1654.5 72627 3047.7
## + parent_educ:lunch_type                  5     349.3 73932 3048.2
## + ethnic_group:parent_marital_status     11    1673.1 72608 3049.5
## + parent_marital_status:practice_sport    6     385.1 73896 3049.9
## + parent_educ:test_prep                   5     113.8 74167 3050.0
## + ethnic_group:practice_sport             8     857.0 73424 3050.1
## + ethnic_group:wkly_study_hours           8     741.7 73539 3051.0
## - parent_marital_status:is_first_child    3    2299.8 76581 3052.9
## + ethnic_group:parent_educ               20    2402.3 71879 3061.5
## 
## Step:  AIC=3037.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:transport_means          2      90.2 74931 3034.1
## - transport_means:wkly_study_hours        2     140.4 74981 3034.5
## - gender:wkly_study_hours                 2     204.9 75046 3035.0
## - gender:practice_sport                   2     215.5 75056 3035.1
## - is_first_child:wkly_study_hours         2     223.2 75064 3035.1
## - gender:lunch_type                       1      15.2 74856 3035.5
## - practice_sport:wkly_study_hours         4     784.5 75625 3035.5
## - gender:is_first_child                   1      33.8 74875 3035.6
## - gender:test_prep                        1      48.7 74889 3035.8
## - gender:transport_means                  1      52.5 74893 3035.8
## - test_prep:is_first_child                1      66.9 74908 3035.9
## - lunch_type:is_first_child               1     106.1 74947 3036.2
## - test_prep:transport_means               1     128.1 74969 3036.4
## - is_first_child:transport_means          1     137.8 74979 3036.4
## - test_prep:practice_sport                2     407.4 75248 3036.6
## - lunch_type:test_prep                    1     182.2 75023 3036.8
## <none>                                                74841 3037.4
## - test_prep:wkly_study_hours              2     520.3 75361 3037.5
## - lunch_type:transport_means              1     325.7 75166 3037.9
## - parent_educ:parent_marital_status      15    4029.3 78870 3038.3
## - lunch_type:wkly_study_hours             2     641.3 75482 3038.4
## - parent_marital_status:transport_means   3     902.6 75743 3038.4
## - ethnic_group:transport_means            4    1226.6 76067 3039.0
## - parent_educ:is_first_child              5    1535.8 76377 3039.3
## + ethnic_group:lunch_type                 4     559.7 74281 3040.9
## + practice_sport:is_first_child           2      47.5 74793 3041.0
## - parent_marital_status:wkly_study_hours  6    2059.5 76900 3041.4
## + ethnic_group:test_prep                  4     468.2 74373 3041.7
## + parent_educ:practice_sport             10    1964.0 72877 3041.7
## + test_prep:parent_marital_status         3     192.8 74648 3041.8
## + ethnic_group:is_first_child             4     439.7 74401 3041.9
## + parent_educ:transport_means             5     683.2 74158 3042.0
## + lunch_type:parent_marital_status        3     164.7 74676 3042.1
## + gender:parent_marital_status            3      61.4 74779 3042.9
## - lunch_type:practice_sport               2    1228.5 76069 3043.0
## + gender:ethnic_group                     4     211.7 74629 3043.7
## + parent_educ:lunch_type                  5     391.3 74449 3044.3
## + gender:parent_educ                      5     376.2 74465 3044.4
## + parent_marital_status:practice_sport    6     466.6 74374 3045.7
## + ethnic_group:practice_sport             8     965.1 73876 3045.7
## + ethnic_group:parent_marital_status     11    1696.6 73144 3045.8
## + parent_educ:wkly_study_hours           10    1444.5 73396 3045.9
## + parent_educ:test_prep                   5     122.2 74719 3046.4
## + ethnic_group:wkly_study_hours           8     794.9 74046 3047.1
## - parent_marital_status:is_first_child    3    2267.8 77109 3049.0
## + ethnic_group:parent_educ               20    2517.8 72323 3057.2
## 
## Step:  AIC=3034.08
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - transport_means:wkly_study_hours        2     152.6 75084 3031.3
## - gender:practice_sport                   2     202.8 75134 3031.7
## - gender:wkly_study_hours                 2     209.1 75140 3031.7
## - is_first_child:wkly_study_hours         2     215.6 75147 3031.8
## - practice_sport:wkly_study_hours         4     763.7 75695 3032.1
## - gender:lunch_type                       1      15.9 74947 3032.2
## - gender:is_first_child                   1      39.1 74970 3032.4
## - gender:test_prep                        1      46.4 74977 3032.4
## - gender:transport_means                  1      52.6 74984 3032.5
## - test_prep:is_first_child                1      65.8 74997 3032.6
## - lunch_type:is_first_child               1     113.8 75045 3033.0
## - test_prep:transport_means               1     124.1 75055 3033.1
## - test_prep:practice_sport                2     399.1 75330 3033.2
## - is_first_child:transport_means          1     157.6 75089 3033.3
## - lunch_type:test_prep                    1     200.4 75131 3033.7
## <none>                                                74931 3034.1
## - test_prep:wkly_study_hours              2     521.1 75452 3034.2
## - lunch_type:transport_means              1     334.9 75266 3034.7
## - parent_educ:parent_marital_status      15    4028.6 78960 3035.0
## - lunch_type:wkly_study_hours             2     635.2 75566 3035.1
## - parent_marital_status:transport_means   3     917.6 75849 3035.3
## - ethnic_group:transport_means            4    1237.8 76169 3035.8
## - parent_educ:is_first_child              5    1530.9 76462 3036.0
## + practice_sport:transport_means          2      90.2 74841 3037.4
## + ethnic_group:lunch_type                 4     545.2 74386 3037.8
## + practice_sport:is_first_child           2      36.5 74894 3037.8
## - parent_marital_status:wkly_study_hours  6    2071.5 77003 3038.2
## + parent_educ:practice_sport             10    1980.6 72950 3038.3
## + ethnic_group:test_prep                  4     468.3 74463 3038.4
## + test_prep:parent_marital_status         3     193.8 74737 3038.6
## + ethnic_group:is_first_child             4     436.2 74495 3038.6
## + lunch_type:parent_marital_status        3     164.8 74766 3038.8
## + parent_educ:transport_means             5     623.6 74307 3039.2
## - lunch_type:practice_sport               2    1207.3 76138 3039.5
## + gender:parent_marital_status            3      49.0 74882 3039.7
## + gender:ethnic_group                     4     211.2 74720 3040.4
## + parent_educ:lunch_type                  5     407.0 74524 3040.9
## + gender:parent_educ                      5     361.2 74570 3041.2
## + parent_marital_status:practice_sport    6     464.0 74467 3042.4
## + ethnic_group:practice_sport             8     951.2 73980 3042.5
## + parent_educ:test_prep                   5     126.5 74805 3043.1
## + ethnic_group:parent_marital_status     11    1608.8 73322 3043.3
## + parent_educ:wkly_study_hours           10    1355.5 73576 3043.3
## + ethnic_group:wkly_study_hours           8     794.8 74136 3043.8
## - parent_marital_status:is_first_child    3    2227.1 77158 3045.4
## + ethnic_group:parent_educ               20    2387.1 72544 3055.0
## 
## Step:  AIC=3031.28
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:wkly_study_hours                 2     200.3 75284 3028.8
## - gender:practice_sport                   2     213.6 75297 3029.0
## - is_first_child:wkly_study_hours         2     235.6 75319 3029.1
## - practice_sport:wkly_study_hours         4     769.9 75854 3029.3
## - gender:lunch_type                       1      13.4 75097 3029.4
## - gender:is_first_child                   1      36.5 75120 3029.6
## - gender:test_prep                        1      36.9 75121 3029.6
## - gender:transport_means                  1      52.0 75136 3029.7
## - test_prep:is_first_child                1      73.0 75157 3029.8
## - test_prep:transport_means               1     106.3 75190 3030.1
## - lunch_type:is_first_child               1     117.0 75201 3030.2
## - is_first_child:transport_means          1     155.5 75239 3030.5
## - test_prep:practice_sport                2     432.0 75516 3030.7
## - lunch_type:test_prep                    1     202.7 75286 3030.9
## - test_prep:wkly_study_hours              2     502.3 75586 3031.2
## <none>                                                75084 3031.3
## - lunch_type:transport_means              1     316.8 75400 3031.8
## - parent_educ:parent_marital_status      15    4009.8 79093 3032.0
## - parent_marital_status:transport_means   3     899.1 75983 3032.3
## - lunch_type:wkly_study_hours             2     642.7 75726 3032.3
## - parent_educ:is_first_child              5    1516.3 76600 3033.1
## - ethnic_group:transport_means            4    1313.2 76397 3033.5
## + transport_means:wkly_study_hours        2     152.6 74931 3034.1
## + practice_sport:transport_means          2     102.4 74981 3034.5
## + ethnic_group:lunch_type                 4     557.6 74526 3034.9
## + practice_sport:is_first_child           2      38.3 75045 3035.0
## + ethnic_group:test_prep                  4     478.7 74605 3035.5
## - parent_marital_status:wkly_study_hours  6    2093.8 77177 3035.5
## + test_prep:parent_marital_status         3     190.2 74893 3035.8
## + ethnic_group:is_first_child             4     437.3 74646 3035.8
## + parent_educ:practice_sport             10    1938.5 73145 3035.8
## + lunch_type:parent_marital_status        3     176.1 74908 3035.9
## + parent_educ:transport_means             5     615.5 74468 3036.4
## - lunch_type:practice_sport               2    1206.4 76290 3036.7
## + gender:parent_marital_status            3      42.7 75041 3036.9
## + gender:ethnic_group                     4     235.5 74848 3037.4
## + parent_educ:lunch_type                  5     412.6 74671 3038.0
## + gender:parent_educ                      5     381.1 74703 3038.3
## + ethnic_group:practice_sport             8     981.1 74103 3039.5
## + parent_marital_status:practice_sport    6     470.9 74613 3039.6
## + parent_educ:test_prep                   5     132.3 74951 3040.2
## + parent_educ:wkly_study_hours           10    1382.8 73701 3040.3
## + ethnic_group:parent_marital_status     11    1599.1 73485 3040.6
## + ethnic_group:wkly_study_hours           8     685.4 74398 3041.9
## - parent_marital_status:is_first_child    3    2151.3 77235 3041.9
## + ethnic_group:parent_educ               20    2409.9 72674 3052.0
## 
## Step:  AIC=3028.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - is_first_child:wkly_study_hours         2     224.7 75509 3026.6
## - gender:practice_sport                   2     227.7 75512 3026.6
## - practice_sport:wkly_study_hours         4     746.4 76030 3026.7
## - gender:lunch_type                       1       9.6 75293 3026.9
## - gender:is_first_child                   1      35.4 75319 3027.1
## - gender:test_prep                        1      54.5 75338 3027.3
## - gender:transport_means                  1      55.2 75339 3027.3
## - test_prep:is_first_child                1      91.8 75376 3027.6
## - lunch_type:is_first_child               1     110.5 75394 3027.7
## - test_prep:transport_means               1     115.1 75399 3027.8
## - is_first_child:transport_means          1     143.5 75427 3028.0
## - test_prep:practice_sport                2     412.6 75696 3028.1
## - lunch_type:test_prep                    1     200.7 75485 3028.4
## - test_prep:wkly_study_hours              2     501.3 75785 3028.8
## <none>                                                75284 3028.8
## - lunch_type:transport_means              1     311.9 75596 3029.3
## - lunch_type:wkly_study_hours             2     588.5 75872 3029.4
## - parent_educ:parent_marital_status      15    4077.9 79362 3030.0
## - parent_marital_status:transport_means   3     918.3 76202 3030.0
## - parent_educ:is_first_child              5    1504.4 76788 3030.5
## - ethnic_group:transport_means            4    1307.8 76592 3031.0
## + gender:wkly_study_hours                 2     200.3 75084 3031.3
## + transport_means:wkly_study_hours        2     143.7 75140 3031.7
## + practice_sport:transport_means          2     106.7 75177 3032.0
## + ethnic_group:lunch_type                 4     564.3 74720 3032.4
## + practice_sport:is_first_child           2      35.0 75249 3032.6
## + ethnic_group:test_prep                  4     500.5 74783 3032.9
## + parent_educ:practice_sport             10    1975.2 73309 3033.2
## + test_prep:parent_marital_status         3     190.2 75094 3033.4
## + lunch_type:parent_marital_status        3     151.8 75132 3033.7
## + ethnic_group:is_first_child             4     393.3 74891 3033.8
## - lunch_type:practice_sport               2    1171.7 76456 3034.0
## + parent_educ:transport_means             5     584.3 74700 3034.2
## + gender:parent_marital_status            3      40.2 75244 3034.5
## - parent_marital_status:wkly_study_hours  6    2307.6 77592 3034.7
## + gender:ethnic_group                     4     245.5 75038 3034.9
## + gender:parent_educ                      5     409.5 74874 3035.6
## + parent_educ:lunch_type                  5     400.9 74883 3035.7
## + ethnic_group:practice_sport             8    1028.4 74255 3036.7
## + parent_marital_status:practice_sport    6     482.3 74802 3037.1
## + parent_educ:wkly_study_hours           10    1462.3 73822 3037.3
## + parent_educ:test_prep                   5     144.3 75140 3037.7
## + ethnic_group:parent_marital_status     11    1560.9 73723 3038.5
## - parent_marital_status:is_first_child    3    2096.8 77381 3039.1
## + ethnic_group:wkly_study_hours           8     665.0 74619 3039.6
## + ethnic_group:parent_educ               20    2348.0 72936 3050.2
## 
## Step:  AIC=3026.61
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:practice_sport                   2     221.8 75730 3024.3
## - gender:lunch_type                       1       8.1 75517 3024.7
## - practice_sport:wkly_study_hours         4     815.9 76325 3024.9
## - gender:is_first_child                   1      47.0 75556 3025.0
## - gender:test_prep                        1      56.0 75565 3025.1
## - gender:transport_means                  1      60.8 75569 3025.1
## - test_prep:is_first_child                1      66.3 75575 3025.1
## - is_first_child:transport_means          1     121.9 75631 3025.6
## - test_prep:practice_sport                2     387.2 75896 3025.6
## - test_prep:transport_means               1     132.1 75641 3025.6
## - lunch_type:is_first_child               1     147.3 75656 3025.8
## - lunch_type:test_prep                    1     226.8 75735 3026.4
## - test_prep:wkly_study_hours              2     504.9 76014 3026.5
## <none>                                                75509 3026.6
## - lunch_type:transport_means              1     315.6 75824 3027.1
## - parent_marital_status:transport_means   3     854.9 76364 3027.2
## - lunch_type:wkly_study_hours             2     599.4 76108 3027.3
## - parent_educ:is_first_child              5    1416.9 76926 3027.6
## - parent_educ:parent_marital_status      15    4118.0 79627 3027.9
## - ethnic_group:transport_means            4    1292.0 76801 3028.6
## + is_first_child:wkly_study_hours         2     224.7 75284 3028.8
## + gender:wkly_study_hours                 2     189.4 75319 3029.1
## + transport_means:wkly_study_hours        2     162.2 75346 3029.3
## + practice_sport:transport_means          2      99.0 75410 3029.8
## + ethnic_group:lunch_type                 4     561.9 74947 3030.2
## + practice_sport:is_first_child           2      29.1 75480 3030.4
## + ethnic_group:test_prep                  4     516.9 74992 3030.6
## + test_prep:parent_marital_status         3     216.2 75292 3030.9
## + parent_educ:practice_sport             10    1970.1 73539 3031.0
## + ethnic_group:is_first_child             4     436.1 75073 3031.2
## + lunch_type:parent_marital_status        3     148.9 75360 3031.4
## + parent_educ:transport_means             5     557.1 74952 3032.2
## + gender:parent_marital_status            3      43.2 75466 3032.3
## + gender:ethnic_group                     4     258.6 75250 3032.6
## - lunch_type:practice_sport               2    1314.3 76823 3032.8
## - parent_marital_status:wkly_study_hours  6    2397.4 77906 3033.1
## + gender:parent_educ                      5     449.5 75059 3033.1
## + parent_educ:lunch_type                  5     402.2 75106 3033.5
## + ethnic_group:practice_sport             8    1054.8 74454 3034.3
## + parent_marital_status:practice_sport    6     535.4 74973 3034.4
## + parent_educ:wkly_study_hours           10    1496.8 74012 3034.8
## + parent_educ:test_prep                   5     130.5 75378 3035.6
## - parent_marital_status:is_first_child    3    2033.1 77542 3036.3
## + ethnic_group:parent_marital_status     11    1481.0 74028 3036.9
## + ethnic_group:wkly_study_hours           8     699.9 74809 3037.1
## + ethnic_group:parent_educ               20    2251.9 73257 3048.8
## 
## Step:  AIC=3024.34
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:is_first_child + gender:transport_means + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:lunch_type                       1       8.4 75739 3022.4
## - test_prep:is_first_child                1      55.9 75786 3022.8
## - gender:is_first_child                   1      57.4 75788 3022.8
## - gender:transport_means                  1      71.5 75802 3022.9
## - gender:test_prep                        1      71.6 75802 3022.9
## - practice_sport:wkly_study_hours         4     886.4 76617 3023.2
## - test_prep:transport_means               1     123.7 75854 3023.3
## - is_first_child:transport_means          1     137.4 75868 3023.4
## - test_prep:practice_sport                2     423.8 76154 3023.6
## - lunch_type:is_first_child               1     180.2 75911 3023.7
## - lunch_type:test_prep                    1     217.8 75948 3024.0
## - test_prep:wkly_study_hours              2     495.1 76226 3024.2
## <none>                                                75730 3024.3
## - parent_marital_status:transport_means   3     814.9 76545 3024.7
## - lunch_type:wkly_study_hours             2     575.3 76306 3024.8
## - lunch_type:transport_means              1     337.3 76068 3025.0
## - parent_educ:is_first_child              5    1435.2 77166 3025.4
## - parent_educ:parent_marital_status      15    4197.3 79928 3026.2
## - ethnic_group:transport_means            4    1300.0 77030 3026.4
## + gender:practice_sport                   2     221.8 75509 3026.6
## + is_first_child:wkly_study_hours         2     218.8 75512 3026.6
## + gender:wkly_study_hours                 2     202.8 75528 3026.8
## + transport_means:wkly_study_hours        2     172.4 75558 3027.0
## + practice_sport:transport_means          2      85.5 75645 3027.7
## + practice_sport:is_first_child           2      28.3 75702 3028.1
## + ethnic_group:lunch_type                 4     527.5 75203 3028.2
## + ethnic_group:test_prep                  4     516.9 75214 3028.3
## + test_prep:parent_marital_status         3     200.8 75530 3028.8
## + ethnic_group:is_first_child             4     413.3 75317 3029.1
## + parent_educ:practice_sport             10    1917.0 73813 3029.2
## + lunch_type:parent_marital_status        3     137.0 75593 3029.3
## + parent_educ:transport_means             5     565.9 75165 3029.9
## + gender:parent_marital_status            3      52.3 75678 3029.9
## - parent_marital_status:wkly_study_hours  6    2321.3 78052 3030.2
## + gender:ethnic_group                     4     216.3 75514 3030.7
## - lunch_type:practice_sport               2    1351.3 77082 3030.8
## + gender:parent_educ                      5     453.1 75277 3030.8
## + parent_educ:lunch_type                  5     416.7 75314 3031.1
## + ethnic_group:practice_sport             8    1124.5 74606 3031.5
## + parent_marital_status:practice_sport    6     558.5 75172 3032.0
## + parent_educ:wkly_study_hours           10    1460.2 74270 3032.8
## + parent_educ:test_prep                   5     130.2 75600 3033.3
## - parent_marital_status:is_first_child    3    2060.2 77791 3034.2
## + ethnic_group:parent_marital_status     11    1515.3 74215 3034.4
## + ethnic_group:wkly_study_hours           8     702.9 75028 3034.8
## + ethnic_group:parent_educ               20    2304.5 73426 3046.1
## 
## Step:  AIC=3022.41
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:is_first_child                   1      57.0 75796 3020.8
## - test_prep:is_first_child                1      57.1 75796 3020.8
## - gender:test_prep                        1      69.1 75808 3020.9
## - gender:transport_means                  1      72.9 75812 3021.0
## - practice_sport:wkly_study_hours         4     884.1 76623 3021.2
## - test_prep:transport_means               1     127.3 75866 3021.4
## - is_first_child:transport_means          1     134.3 75873 3021.4
## - test_prep:practice_sport                2     429.7 76169 3021.7
## - lunch_type:is_first_child               1     182.4 75921 3021.8
## - lunch_type:test_prep                    1     226.2 75965 3022.2
## - test_prep:wkly_study_hours              2     500.1 76239 3022.3
## <none>                                                75739 3022.4
## - parent_marital_status:transport_means   3     808.4 76547 3022.7
## - lunch_type:wkly_study_hours             2     572.3 76311 3022.8
## - lunch_type:transport_means              1     345.8 76085 3023.1
## - parent_educ:is_first_child              5    1434.6 77173 3023.5
## - parent_educ:parent_marital_status      15    4194.5 79933 3024.2
## + gender:lunch_type                       1       8.4 75730 3024.3
## - ethnic_group:transport_means            4    1313.0 77052 3024.6
## + gender:practice_sport                   2     222.1 75517 3024.7
## + is_first_child:wkly_study_hours         2     217.1 75522 3024.7
## + gender:wkly_study_hours                 2     199.5 75539 3024.8
## + transport_means:wkly_study_hours        2     170.3 75569 3025.1
## + practice_sport:transport_means          2      85.8 75653 3025.7
## + practice_sport:is_first_child           2      28.3 75711 3026.2
## + ethnic_group:lunch_type                 4     527.2 75212 3026.3
## + ethnic_group:test_prep                  4     519.0 75220 3026.3
## + test_prep:parent_marital_status         3     203.5 75535 3026.8
## + ethnic_group:is_first_child             4     409.1 75330 3027.2
## + lunch_type:parent_marital_status        3     142.1 75597 3027.3
## + parent_educ:practice_sport             10    1903.8 73835 3027.4
## + parent_educ:transport_means             5     572.4 75166 3027.9
## + gender:parent_marital_status            3      51.1 75688 3028.0
## - parent_marital_status:wkly_study_hours  6    2359.0 78098 3028.5
## + gender:ethnic_group                     4     216.1 75523 3028.7
## + gender:parent_educ                      5     450.2 75289 3028.9
## + parent_educ:lunch_type                  5     424.1 75315 3029.1
## - lunch_type:practice_sport               2    1386.6 77125 3029.1
## + ethnic_group:practice_sport             8    1102.7 74636 3029.8
## + parent_marital_status:practice_sport    6     554.6 75184 3030.1
## + parent_educ:wkly_study_hours           10    1456.2 74283 3030.9
## + parent_educ:test_prep                   5     128.7 75610 3031.4
## - parent_marital_status:is_first_child    3    2051.8 77791 3032.2
## + ethnic_group:parent_marital_status     11    1513.5 74225 3032.5
## + ethnic_group:wkly_study_hours           8     705.0 75034 3032.9
## + ethnic_group:parent_educ               20    2265.2 73474 3044.5
## 
## Step:  AIC=3020.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:transport_means + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:test_prep                        1      63.1 75859 3019.3
## - test_prep:is_first_child                1      65.8 75862 3019.4
## - gender:transport_means                  1      71.8 75868 3019.4
## - is_first_child:transport_means          1     124.6 75921 3019.8
## - test_prep:transport_means               1     129.3 75925 3019.8
## - practice_sport:wkly_study_hours         4     920.1 76716 3020.0
## - test_prep:practice_sport                2     414.2 76210 3020.1
## - lunch_type:is_first_child               1     171.5 75967 3020.2
## - test_prep:wkly_study_hours              2     490.6 76286 3020.7
## - lunch_type:test_prep                    1     235.7 76032 3020.7
## <none>                                                75796 3020.8
## - lunch_type:wkly_study_hours             2     573.9 76370 3021.3
## - parent_marital_status:transport_means   3     837.6 76634 3021.3
## - lunch_type:transport_means              1     365.6 76161 3021.7
## - parent_educ:is_first_child              5    1471.7 77268 3022.2
## + gender:is_first_child                   1      57.0 75739 3022.4
## - parent_educ:parent_marital_status      15    4190.6 79986 3022.6
## + gender:lunch_type                       1       8.1 75788 3022.8
## + gender:practice_sport                   2     232.2 75564 3023.0
## + is_first_child:wkly_study_hours         2     230.4 75565 3023.1
## + gender:wkly_study_hours                 2     198.3 75598 3023.3
## - ethnic_group:transport_means            4    1355.1 77151 3023.3
## + transport_means:wkly_study_hours        2     165.8 75630 3023.6
## + practice_sport:transport_means          2      91.4 75704 3024.1
## + practice_sport:is_first_child           2      30.8 75765 3024.6
## + ethnic_group:lunch_type                 4     528.1 75268 3024.7
## + ethnic_group:test_prep                  4     488.7 75307 3025.0
## + test_prep:parent_marital_status         3     207.7 75588 3025.2
## + lunch_type:parent_marital_status        3     150.2 75646 3025.7
## + parent_educ:practice_sport             10    1908.4 73887 3025.8
## + ethnic_group:is_first_child             4     370.0 75426 3026.0
## + gender:parent_marital_status            3      58.6 75737 3026.4
## + parent_educ:transport_means             5     568.5 75227 3026.4
## - parent_marital_status:wkly_study_hours  6    2312.6 78108 3026.6
## + gender:ethnic_group                     4     219.5 75576 3027.1
## + parent_educ:lunch_type                  5     453.2 75343 3027.3
## + gender:parent_educ                      5     447.8 75348 3027.3
## - lunch_type:practice_sport               2    1433.9 77230 3027.9
## + ethnic_group:practice_sport             8    1075.1 74721 3028.4
## + parent_marital_status:practice_sport    6     536.8 75259 3028.7
## + parent_educ:wkly_study_hours           10    1464.0 74332 3029.3
## + parent_educ:test_prep                   5     129.7 75666 3029.8
## - parent_marital_status:is_first_child    3    2041.9 77838 3030.5
## + ethnic_group:parent_marital_status     11    1532.8 74263 3030.8
## + ethnic_group:wkly_study_hours           8     698.7 75097 3031.4
## + ethnic_group:parent_educ               20    2190.8 73605 3043.5
## 
## Step:  AIC=3019.34
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:transport_means + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:transport_means                  1      61.1 75920 3017.8
## - test_prep:is_first_child                1      66.6 75926 3017.9
## - is_first_child:transport_means          1     121.1 75980 3018.3
## - test_prep:transport_means               1     123.3 75982 3018.3
## - practice_sport:wkly_study_hours         4     907.1 76766 3018.3
## - test_prep:practice_sport                2     408.5 76267 3018.5
## - lunch_type:is_first_child               1     162.8 76022 3018.6
## - test_prep:wkly_study_hours              2     472.7 76332 3019.0
## - lunch_type:test_prep                    1     249.1 76108 3019.3
## <none>                                                75859 3019.3
## - lunch_type:wkly_study_hours             2     582.1 76441 3019.8
## - parent_marital_status:transport_means   3     852.8 76712 3019.9
## - lunch_type:transport_means              1     379.7 76239 3020.3
## - parent_educ:is_first_child              5    1449.5 77308 3020.5
## - parent_educ:parent_marital_status      15    4159.3 80018 3020.8
## + gender:test_prep                        1      63.1 75796 3020.8
## + gender:is_first_child                   1      51.0 75808 3020.9
## + gender:lunch_type                       1       5.8 75853 3021.3
## + gender:practice_sport                   2     246.4 75613 3021.4
## + is_first_child:wkly_study_hours         2     231.2 75628 3021.5
## + gender:wkly_study_hours                 2     218.9 75640 3021.6
## - ethnic_group:transport_means            4    1372.6 77232 3021.9
## + transport_means:wkly_study_hours        2     153.6 75705 3022.1
## + practice_sport:transport_means          2      88.4 75771 3022.7
## + practice_sport:is_first_child           2      33.0 75826 3023.1
## + ethnic_group:lunch_type                 4     538.8 75320 3023.1
## + ethnic_group:test_prep                  4     464.8 75394 3023.7
## + test_prep:parent_marital_status         3     205.5 75653 3023.7
## + lunch_type:parent_marital_status        3     157.5 75702 3024.1
## + parent_educ:practice_sport             10    1925.9 73933 3024.2
## + ethnic_group:is_first_child             4     351.2 75508 3024.6
## - parent_marital_status:wkly_study_hours  6    2281.3 78140 3024.8
## + gender:parent_marital_status            3      61.3 75798 3024.9
## + parent_educ:transport_means             5     558.7 75300 3025.0
## + gender:ethnic_group                     4     231.9 75627 3025.5
## + gender:parent_educ                      5     446.9 75412 3025.8
## + parent_educ:lunch_type                  5     444.2 75415 3025.9
## - lunch_type:practice_sport               2    1417.7 77277 3026.3
## + parent_marital_status:practice_sport    6     550.5 75308 3027.0
## + ethnic_group:practice_sport             8    1054.5 74804 3027.1
## + parent_educ:wkly_study_hours           10    1478.9 74380 3027.7
## + parent_educ:test_prep                   5     132.2 75727 3028.3
## - parent_marital_status:is_first_child    3    2002.0 77861 3028.7
## + ethnic_group:parent_marital_status     11    1567.5 74291 3029.0
## + ethnic_group:wkly_study_hours           8     725.0 75134 3029.7
## + ethnic_group:parent_educ               20    2197.5 73662 3042.0
## 
## Step:  AIC=3017.81
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:is_first_child                1      71.6 75992 3016.4
## - practice_sport:wkly_study_hours         4     888.2 76808 3016.7
## - is_first_child:transport_means          1     131.9 76052 3016.8
## - test_prep:transport_means               1     138.8 76059 3016.9
## - test_prep:practice_sport                2     403.4 76323 3016.9
## - lunch_type:is_first_child               1     150.7 76071 3017.0
## - test_prep:wkly_study_hours              2     477.5 76397 3017.5
## - lunch_type:test_prep                    1     253.8 76174 3017.8
## <none>                                                75920 3017.8
## - lunch_type:wkly_study_hours             2     565.9 76486 3018.2
## - parent_marital_status:transport_means   3     851.0 76771 3018.4
## - parent_educ:is_first_child              5    1432.0 77352 3018.8
## - lunch_type:transport_means              1     393.6 76314 3018.9
## - parent_educ:parent_marital_status      15    4127.3 80047 3019.1
## + gender:transport_means                  1      61.1 75859 3019.3
## + gender:test_prep                        1      52.4 75868 3019.4
## + gender:is_first_child                   1      50.5 75870 3019.4
## + gender:lunch_type                       1       7.1 75913 3019.8
## + gender:practice_sport                   2     255.3 75665 3019.8
## + is_first_child:wkly_study_hours         2     236.9 75683 3020.0
## + gender:wkly_study_hours                 2     221.6 75698 3020.1
## - ethnic_group:transport_means            4    1335.2 77255 3020.1
## + transport_means:wkly_study_hours        2     154.0 75766 3020.6
## + practice_sport:transport_means          2      89.3 75831 3021.1
## + practice_sport:is_first_child           2      37.7 75882 3021.5
## + ethnic_group:lunch_type                 4     532.3 75388 3021.7
## + ethnic_group:test_prep                  4     467.3 75453 3022.2
## + test_prep:parent_marital_status         3     200.6 75719 3022.2
## + parent_educ:practice_sport             10    1954.7 73965 3022.4
## + lunch_type:parent_marital_status        3     160.5 75760 3022.6
## + ethnic_group:is_first_child             4     355.2 75565 3023.1
## - parent_marital_status:wkly_study_hours  6    2270.6 78191 3023.2
## + gender:parent_marital_status            3      59.3 75861 3023.3
## + parent_educ:transport_means             5     560.2 75360 3023.4
## + gender:ethnic_group                     4     247.9 75672 3023.9
## + gender:parent_educ                      5     449.9 75470 3024.3
## + parent_educ:lunch_type                  5     448.9 75471 3024.3
## - lunch_type:practice_sport               2    1396.7 77317 3024.6
## + parent_marital_status:practice_sport    6     550.3 75370 3025.5
## + ethnic_group:practice_sport             8    1036.1 74884 3025.7
## + parent_educ:wkly_study_hours           10    1435.0 74485 3026.6
## + parent_educ:test_prep                   5     128.0 75792 3026.8
## + ethnic_group:parent_marital_status     11    1602.7 74317 3027.2
## - parent_marital_status:is_first_child    3    2036.3 77956 3027.4
## + ethnic_group:wkly_study_hours           8     718.1 75202 3028.2
## + ethnic_group:parent_educ               20    2173.1 73747 3040.7
## - gender                                  1   12750.1 88670 3107.4
## 
## Step:  AIC=3016.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:wkly_study_hours         4     915.5 76907 3015.4
## - is_first_child:transport_means          1     140.3 76132 3015.5
## - test_prep:transport_means               1     140.4 76132 3015.5
## - test_prep:practice_sport                2     403.2 76395 3015.5
## - lunch_type:is_first_child               1     166.0 76158 3015.7
## - test_prep:wkly_study_hours              2     471.7 76463 3016.0
## - lunch_type:test_prep                    1     244.8 76236 3016.3
## <none>                                                75992 3016.4
## - parent_marital_status:transport_means   3     837.7 76829 3016.8
## - lunch_type:wkly_study_hours             2     582.5 76574 3016.9
## - parent_educ:is_first_child              5    1386.8 77378 3017.0
## - parent_educ:parent_marital_status      15    4132.9 80125 3017.6
## - lunch_type:transport_means              1     429.9 76421 3017.7
## + test_prep:is_first_child                1      71.6 75920 3017.8
## + gender:transport_means                  1      66.1 75926 3017.9
## + gender:is_first_child                   1      59.1 75933 3017.9
## + gender:test_prep                        1      52.7 75939 3018.0
## + gender:lunch_type                       1       8.3 75983 3018.3
## + gender:practice_sport                   2     244.1 75748 3018.5
## + gender:wkly_study_hours                 2     240.2 75751 3018.5
## - ethnic_group:transport_means            4    1326.3 77318 3018.6
## + is_first_child:wkly_study_hours         2     213.2 75778 3018.7
## + transport_means:wkly_study_hours        2     158.8 75833 3019.1
## + practice_sport:transport_means          2      91.2 75900 3019.7
## + practice_sport:is_first_child           2      28.3 75963 3020.2
## + ethnic_group:lunch_type                 4     528.2 75463 3020.3
## + test_prep:parent_marital_status         3     219.9 75772 3020.7
## + ethnic_group:test_prep                  4     467.8 75524 3020.7
## + parent_educ:practice_sport             10    1968.3 74023 3020.9
## + lunch_type:parent_marital_status        3     163.3 75828 3021.1
## + ethnic_group:is_first_child             4     365.5 75626 3021.5
## - parent_marital_status:wkly_study_hours  6    2263.7 78255 3021.7
## + parent_educ:transport_means             5     583.3 75408 3021.8
## + gender:parent_marital_status            3      64.3 75927 3021.9
## + gender:ethnic_group                     4     233.9 75758 3022.6
## + gender:parent_educ                      5     453.0 75539 3022.8
## + parent_educ:lunch_type                  5     439.7 75552 3022.9
## - lunch_type:practice_sport               2    1447.7 77439 3023.5
## + parent_marital_status:practice_sport    6     544.3 75447 3024.1
## + ethnic_group:practice_sport             8    1040.0 74952 3024.2
## + parent_educ:wkly_study_hours           10    1447.2 74544 3025.0
## + parent_educ:test_prep                   5     136.2 75855 3025.3
## - parent_marital_status:is_first_child    3    1998.8 77990 3025.7
## + ethnic_group:parent_marital_status     11    1600.7 74391 3025.8
## + ethnic_group:wkly_study_hours           8     727.9 75264 3026.7
## + ethnic_group:parent_educ               20    2203.3 73788 3039.0
## - gender                                  1   12874.8 88866 3106.7
## 
## Step:  AIC=3015.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:is_first_child               1     112.2 77019 3014.3
## - is_first_child:transport_means          1     131.0 77038 3014.4
## - test_prep:transport_means               1     140.5 77048 3014.5
## - parent_educ:is_first_child              5    1213.8 78121 3014.7
## - test_prep:practice_sport                2     447.6 77355 3014.9
## <none>                                                76907 3015.4
## - test_prep:wkly_study_hours              2     530.7 77438 3015.5
## - lunch_type:wkly_study_hours             2     537.6 77445 3015.6
## - lunch_type:test_prep                    1     292.2 77199 3015.7
## - parent_marital_status:transport_means   3     855.9 77763 3016.0
## - parent_educ:parent_marital_status      15    4099.1 81006 3016.1
## - lunch_type:transport_means              1     378.0 77285 3016.3
## + practice_sport:wkly_study_hours         4     915.5 75992 3016.4
## + test_prep:is_first_child                1      98.9 76808 3016.7
## + gender:is_first_child                   1      98.6 76808 3016.7
## - ethnic_group:transport_means            4    1240.6 78148 3016.9
## + gender:practice_sport                   2     316.3 76591 3017.0
## + gender:transport_means                  1      46.6 76860 3017.1
## + gender:test_prep                        1      42.4 76865 3017.1
## + is_first_child:wkly_study_hours         2     284.8 76622 3017.2
## + gender:lunch_type                       1       6.1 76901 3017.4
## + gender:wkly_study_hours                 2     223.6 76683 3017.7
## + transport_means:wkly_study_hours        2     181.5 76726 3018.0
## + practice_sport:transport_means          2      74.7 76832 3018.9
## + practice_sport:is_first_child           2      50.1 76857 3019.1
## + ethnic_group:test_prep                  4     485.1 76422 3019.7
## + test_prep:parent_marital_status         3     175.0 76732 3020.1
## + ethnic_group:lunch_type                 4     427.3 76480 3020.2
## + parent_educ:transport_means             5     659.0 76248 3020.4
## + ethnic_group:is_first_child             4     398.8 76508 3020.4
## + lunch_type:parent_marital_status        3     136.8 76770 3020.4
## + gender:parent_marital_status            3      70.3 76837 3020.9
## + parent_educ:practice_sport             10    1831.0 75076 3021.2
## + parent_educ:lunch_type                  5     538.8 76368 3021.3
## - parent_marital_status:wkly_study_hours  6    2382.5 79290 3021.4
## + gender:parent_educ                      5     483.0 76424 3021.7
## + gender:ethnic_group                     4     222.0 76685 3021.7
## - lunch_type:practice_sport               2    1420.3 78327 3022.2
## + parent_marital_status:practice_sport    6     507.1 76400 3023.5
## + ethnic_group:practice_sport             8     971.4 75936 3023.9
## - parent_marital_status:is_first_child    3    1939.7 78847 3024.1
## + parent_educ:test_prep                   5     141.9 76765 3024.3
## + parent_educ:wkly_study_hours           10    1326.1 75581 3025.2
## + ethnic_group:wkly_study_hours           8     766.2 76141 3025.5
## + ethnic_group:parent_marital_status     11    1519.3 75388 3025.7
## + ethnic_group:parent_educ               20    2096.4 74811 3039.1
## - gender                                  1   12541.2 89448 3102.6
## 
## Step:  AIC=3014.3
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:transport_means               1     124.8 77144 3013.2
## - is_first_child:transport_means          1     128.6 77148 3013.3
## - parent_educ:is_first_child              5    1211.9 78231 3013.5
## - test_prep:practice_sport                2     461.2 77481 3013.8
## - test_prep:wkly_study_hours              2     519.7 77539 3014.3
## <none>                                                77019 3014.3
## - lunch_type:wkly_study_hours             2     554.4 77574 3014.5
## - lunch_type:test_prep                    1     300.8 77320 3014.6
## - parent_marital_status:transport_means   3     840.4 77860 3014.7
## - lunch_type:transport_means              1     363.1 77382 3015.1
## - parent_educ:parent_marital_status      15    4150.6 81170 3015.3
## + lunch_type:is_first_child               1     112.2 76907 3015.4
## + test_prep:is_first_child                1     111.9 76907 3015.4
## + gender:is_first_child                   1      87.1 76932 3015.6
## + practice_sport:wkly_study_hours         4     861.7 76158 3015.7
## + gender:practice_sport                   2     343.3 76676 3015.7
## - ethnic_group:transport_means            4    1239.7 78259 3015.7
## + is_first_child:wkly_study_hours         2     316.6 76703 3015.9
## + gender:transport_means                  1      38.4 76981 3016.0
## + gender:test_prep                        1      38.3 76981 3016.0
## + gender:lunch_type                       1       7.9 77011 3016.2
## + gender:wkly_study_hours                 2     220.2 76799 3016.6
## + transport_means:wkly_study_hours        2     189.0 76830 3016.8
## + practice_sport:transport_means          2      81.6 76938 3017.7
## + practice_sport:is_first_child           2      54.8 76965 3017.9
## + ethnic_group:test_prep                  4     488.8 76530 3018.5
## + ethnic_group:is_first_child             4     441.0 76578 3018.9
## + test_prep:parent_marital_status         3     175.7 76844 3018.9
## + ethnic_group:lunch_type                 4     416.5 76603 3019.1
## + lunch_type:parent_marital_status        3     133.8 76886 3019.3
## + parent_educ:transport_means             5     649.1 76370 3019.3
## + gender:parent_marital_status            3      64.9 76954 3019.8
## + parent_educ:practice_sport             10    1810.2 75209 3020.3
## + parent_educ:lunch_type                  5     522.4 76497 3020.3
## + gender:ethnic_group                     4     235.2 76784 3020.5
## + gender:parent_educ                      5     491.0 76528 3020.5
## - parent_marital_status:wkly_study_hours  6    2433.8 79453 3020.7
## - lunch_type:practice_sport               2    1430.6 78450 3021.2
## + ethnic_group:practice_sport             8     970.5 76049 3022.8
## + parent_marital_status:practice_sport    6     428.5 76591 3023.0
## + parent_educ:test_prep                   5     143.4 76876 3023.2
## - parent_marital_status:is_first_child    3    2057.4 79077 3023.8
## + parent_educ:wkly_study_hours           10    1304.5 75715 3024.2
## + ethnic_group:wkly_study_hours           8     774.1 76245 3024.3
## + ethnic_group:parent_marital_status     11    1464.4 75555 3025.0
## + ethnic_group:parent_educ               20    2101.3 74918 3038.0
## - gender                                  1   12517.3 89537 3101.2
## 
## Step:  AIC=3013.25
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - is_first_child:transport_means          1     144.1 77288 3012.3
## - parent_educ:is_first_child              5    1232.2 78376 3012.6
## - test_prep:practice_sport                2     465.7 77610 3012.8
## - lunch_type:wkly_study_hours             2     493.4 77638 3013.0
## - test_prep:wkly_study_hours              2     504.4 77648 3013.1
## <none>                                                77144 3013.2
## - lunch_type:test_prep                    1     306.8 77451 3013.6
## - parent_marital_status:transport_means   3     855.0 77999 3013.8
## - lunch_type:transport_means              1     345.9 77490 3013.9
## + test_prep:transport_means               1     124.8 77019 3014.3
## + test_prep:is_first_child                1     112.4 77032 3014.4
## + lunch_type:is_first_child               1      96.5 77048 3014.5
## + gender:is_first_child                   1      90.9 77053 3014.6
## + practice_sport:wkly_study_hours         4     867.3 76277 3014.6
## + is_first_child:wkly_study_hours         2     335.0 76809 3014.7
## + gender:practice_sport                   2     333.9 76810 3014.7
## - parent_educ:parent_marital_status      15    4230.9 81375 3014.8
## + gender:transport_means                  1      51.1 77093 3014.9
## + gender:test_prep                        1      33.7 77110 3015.0
## - ethnic_group:transport_means            4    1302.9 78447 3015.1
## + gender:lunch_type                       1      11.5 77133 3015.2
## + gender:wkly_study_hours                 2     229.6 76915 3015.5
## + transport_means:wkly_study_hours        2     164.7 76979 3016.0
## + practice_sport:transport_means          2      74.8 77069 3016.7
## + practice_sport:is_first_child           2      51.2 77093 3016.9
## + ethnic_group:test_prep                  4     518.1 76626 3017.3
## + test_prep:parent_marital_status         3     193.8 76950 3017.8
## + ethnic_group:lunch_type                 4     426.6 76718 3018.0
## + parent_educ:transport_means             5     682.3 76462 3018.0
## + ethnic_group:is_first_child             4     417.4 76727 3018.1
## + lunch_type:parent_marital_status        3     140.0 77004 3018.2
## + gender:parent_marital_status            3      62.0 77082 3018.8
## + parent_educ:lunch_type                  5     527.7 76616 3019.2
## + parent_educ:practice_sport             10    1795.9 75348 3019.3
## + gender:ethnic_group                     4     244.1 76900 3019.4
## + gender:parent_educ                      5     499.9 76644 3019.4
## - parent_marital_status:wkly_study_hours  6    2412.6 79557 3019.4
## - lunch_type:practice_sport               2    1455.1 78599 3020.3
## + ethnic_group:practice_sport             8     984.2 76160 3021.7
## + parent_marital_status:practice_sport    6     418.9 76725 3022.0
## + parent_educ:test_prep                   5     144.9 76999 3022.1
## - parent_marital_status:is_first_child    3    2069.6 79214 3022.9
## + parent_educ:wkly_study_hours           10    1307.3 75837 3023.2
## + ethnic_group:wkly_study_hours           8     770.1 76374 3023.3
## + ethnic_group:parent_marital_status     11    1459.7 75684 3024.0
## + ethnic_group:parent_educ               20    2023.1 75121 3037.6
## - gender                                  1   12401.3 89545 3099.2
## 
## Step:  AIC=3012.35
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:practice_sport                2     469.3 77757 3011.9
## - parent_educ:is_first_child              5    1272.3 78560 3012.0
## - test_prep:wkly_study_hours              2     508.1 77796 3012.2
## - lunch_type:wkly_study_hours             2     524.0 77812 3012.3
## <none>                                                77288 3012.3
## - lunch_type:test_prep                    1     272.9 77561 3012.4
## - lunch_type:transport_means              1     336.5 77625 3012.9
## + is_first_child:transport_means          1     144.1 77144 3013.2
## + test_prep:transport_means               1     140.3 77148 3013.3
## + test_prep:is_first_child                1     122.9 77165 3013.4
## + lunch_type:is_first_child               1      93.2 77195 3013.6
## + gender:practice_sport                   2     346.5 76942 3013.7
## - parent_marital_status:transport_means   3     971.0 78259 3013.7
## + gender:is_first_child                   1      78.7 77209 3013.8
## + practice_sport:wkly_study_hours         4     859.2 76429 3013.8
## - parent_educ:parent_marital_status      15    4238.5 81527 3013.8
## + gender:transport_means                  1      62.3 77226 3013.9
## + is_first_child:wkly_study_hours         2     301.1 76987 3014.1
## + gender:test_prep                        1      30.1 77258 3014.1
## + gender:lunch_type                       1       8.4 77280 3014.3
## - ethnic_group:transport_means            4    1313.4 78602 3014.3
## + gender:wkly_study_hours                 2     218.6 77070 3014.7
## + transport_means:wkly_study_hours        2     163.3 77125 3015.1
## + practice_sport:transport_means          2      89.4 77199 3015.7
## + practice_sport:is_first_child           2      64.9 77223 3015.9
## + ethnic_group:test_prep                  4     542.2 76746 3016.2
## + test_prep:parent_marital_status         3     183.1 77105 3016.9
## + ethnic_group:lunch_type                 4     413.2 76875 3017.2
## + lunch_type:parent_marital_status        3     139.1 77149 3017.3
## + parent_educ:transport_means             5     635.8 76652 3017.5
## + gender:parent_marital_status            3      80.3 77208 3017.7
## + ethnic_group:is_first_child             4     330.6 76958 3017.8
## + parent_educ:lunch_type                  5     529.8 76758 3018.3
## + gender:ethnic_group                     4     247.6 77041 3018.5
## + gender:parent_educ                      5     496.8 76791 3018.6
## - parent_marital_status:wkly_study_hours  6    2429.0 79717 3018.6
## + parent_educ:practice_sport             10    1711.9 75576 3019.1
## - lunch_type:practice_sport               2    1445.6 78734 3019.3
## + ethnic_group:practice_sport             8    1012.9 76275 3020.6
## + parent_educ:test_prep                   5     179.0 77109 3021.0
## + parent_marital_status:practice_sport    6     437.9 76850 3021.0
## - parent_marital_status:is_first_child    3    2038.1 79326 3021.7
## + parent_educ:wkly_study_hours           10    1301.9 75986 3022.3
## + ethnic_group:wkly_study_hours           8     781.1 76507 3022.4
## + ethnic_group:parent_marital_status     11    1531.4 75757 3022.6
## + ethnic_group:parent_educ               20    1990.8 75297 3037.0
## - gender                                  1   12297.8 89586 3097.5
## 
## Step:  AIC=3011.92
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:wkly_study_hours              2     503.4 78261 3011.7
## <none>                                                77757 3011.9
## - lunch_type:test_prep                    1     290.1 78048 3012.1
## - lunch_type:transport_means              1     318.4 78076 3012.3
## + test_prep:practice_sport                2     469.3 77288 3012.3
## - lunch_type:wkly_study_hours             2     588.6 78346 3012.4
## - parent_educ:parent_marital_status      15    4157.8 81915 3012.7
## + is_first_child:transport_means          1     147.6 77610 3012.8
## + test_prep:transport_means               1     145.3 77612 3012.8
## + test_prep:is_first_child                1     122.2 77635 3013.0
## + gender:practice_sport                   2     383.7 77374 3013.0
## - parent_educ:is_first_child              5    1477.9 79235 3013.0
## - parent_marital_status:transport_means   3     950.8 78708 3013.1
## + lunch_type:is_first_child               1     106.0 77652 3013.1
## + practice_sport:wkly_study_hours         4     891.5 76866 3013.1
## - ethnic_group:transport_means            4    1242.4 79000 3013.3
## + gender:is_first_child                   1      59.5 77698 3013.5
## + gender:transport_means                  1      54.2 77703 3013.5
## + gender:test_prep                        1      25.3 77732 3013.7
## + gender:lunch_type                       1      15.2 77742 3013.8
## + is_first_child:wkly_study_hours         2     265.7 77492 3013.9
## + transport_means:wkly_study_hours        2     199.8 77558 3014.4
## + gender:wkly_study_hours                 2     198.7 77559 3014.4
## + practice_sport:is_first_child           2      85.8 77672 3015.3
## + practice_sport:transport_means          2      82.6 77675 3015.3
## + test_prep:parent_marital_status         3     234.8 77523 3016.1
## + ethnic_group:lunch_type                 4     460.3 77297 3016.4
## + ethnic_group:test_prep                  4     451.0 77306 3016.5
## + lunch_type:parent_marital_status        3     142.6 77615 3016.8
## + parent_educ:transport_means             5     666.7 77091 3016.8
## + gender:parent_marital_status            3     101.5 77656 3017.2
## + ethnic_group:is_first_child             4     337.2 77420 3017.4
## - parent_marital_status:wkly_study_hours  6    2359.6 80117 3017.6
## + parent_educ:lunch_type                  5     553.5 77204 3017.7
## + gender:parent_educ                      5     531.7 77226 3017.9
## + gender:ethnic_group                     4     217.0 77540 3018.3
## + parent_educ:practice_sport             10    1673.0 76084 3019.1
## - lunch_type:practice_sport               2    1545.1 79303 3019.5
## - parent_marital_status:is_first_child    3    1928.4 79686 3020.4
## + ethnic_group:practice_sport             8     981.3 76776 3020.4
## + parent_marital_status:practice_sport    6     444.5 77313 3020.5
## + parent_educ:test_prep                   5     146.8 77611 3020.8
## + parent_educ:wkly_study_hours           10    1371.1 76386 3021.4
## + ethnic_group:wkly_study_hours           8     769.9 76988 3022.1
## + ethnic_group:parent_marital_status     11    1497.6 76260 3022.4
## + ethnic_group:parent_educ               20    2102.3 75655 3035.8
## - gender                                  1   12364.6 90122 3097.0
## 
## Step:  AIC=3011.73
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:transport_means              1     221.7 78483 3011.4
## <none>                                                78261 3011.7
## + test_prep:wkly_study_hours              2     503.4 77757 3011.9
## - parent_educ:parent_marital_status      15    4125.9 82387 3012.0
## - lunch_type:test_prep                    1     312.1 78573 3012.1
## + test_prep:practice_sport                2     464.6 77796 3012.2
## - ethnic_group:transport_means            4    1170.1 79431 3012.5
## + practice_sport:wkly_study_hours         4     942.3 77319 3012.6
## + is_first_child:transport_means          1     151.9 78109 3012.6
## - lunch_type:wkly_study_hours             2     649.4 78910 3012.6
## + test_prep:transport_means               1     129.4 78132 3012.8
## + test_prep:is_first_child                1     116.8 78144 3012.8
## - parent_marital_status:transport_means   3     952.4 79213 3012.9
## - parent_educ:is_first_child              5    1493.3 79754 3012.9
## + gender:practice_sport                   2     370.4 77890 3012.9
## + lunch_type:is_first_child               1      98.9 78162 3013.0
## + gender:transport_means                  1      60.3 78201 3013.3
## + gender:is_first_child                   1      51.3 78210 3013.3
## + gender:lunch_type                       1      22.1 78239 3013.6
## + gender:test_prep                        1      14.9 78246 3013.6
## + is_first_child:wkly_study_hours         2     273.1 77988 3013.7
## + gender:wkly_study_hours                 2     195.1 78066 3014.3
## + transport_means:wkly_study_hours        2     185.5 78075 3014.3
## + practice_sport:transport_means          2      85.5 78175 3015.1
## + practice_sport:is_first_child           2      56.2 78205 3015.3
## + ethnic_group:test_prep                  4     507.3 77754 3015.9
## + test_prep:parent_marital_status         3     218.3 78043 3016.1
## + ethnic_group:lunch_type                 4     477.5 77783 3016.1
## + parent_educ:transport_means             5     668.9 77592 3016.7
## + lunch_type:parent_marital_status        3     124.1 78137 3016.8
## + gender:parent_marital_status            3     110.8 78150 3016.9
## - parent_marital_status:wkly_study_hours  6    2347.2 80608 3017.2
## + gender:parent_educ                      5     531.0 77730 3017.7
## + parent_educ:lunch_type                  5     527.0 77734 3017.8
## + gender:ethnic_group                     4     259.9 78001 3017.8
## + ethnic_group:is_first_child             4     236.4 78024 3017.9
## - lunch_type:practice_sport               2    1430.9 79692 3018.4
## + parent_marital_status:practice_sport    6     469.5 77791 3020.2
## + parent_educ:practice_sport             10    1509.6 76751 3020.2
## + parent_educ:test_prep                   5     187.2 78074 3020.3
## + parent_educ:wkly_study_hours           10    1467.4 76794 3020.6
## - parent_marital_status:is_first_child    3    2024.8 80286 3020.8
## + ethnic_group:practice_sport             8     898.6 77362 3020.9
## + ethnic_group:parent_marital_status     11    1610.1 76651 3021.5
## + ethnic_group:wkly_study_hours           8     778.1 77483 3021.8
## + ethnic_group:parent_educ               20    2152.2 76109 3035.3
## - gender                                  1   12415.3 90676 3096.6
## 
## Step:  AIC=3011.4
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:test_prep                    1     262.1 78745 3011.4
## <none>                                                78483 3011.4
## - parent_educ:parent_marital_status      15    4130.4 82613 3011.7
## + lunch_type:transport_means              1     221.7 78261 3011.7
## + test_prep:practice_sport                2     449.9 78033 3012.0
## - ethnic_group:transport_means            4    1161.5 79644 3012.1
## - lunch_type:wkly_study_hours             2     628.3 79111 3012.1
## - parent_educ:is_first_child              5    1457.2 79940 3012.2
## + test_prep:is_first_child                1     146.9 78336 3012.3
## + is_first_child:transport_means          1     144.0 78339 3012.3
## + test_prep:wkly_study_hours              2     406.7 78076 3012.3
## + gender:practice_sport                   2     390.3 78092 3012.5
## + test_prep:transport_means               1     116.1 78367 3012.5
## - parent_marital_status:transport_means   3     954.6 79437 3012.5
## + practice_sport:wkly_study_hours         4     897.3 77585 3012.6
## + lunch_type:is_first_child               1      89.8 78393 3012.7
## + gender:transport_means                  1      71.0 78412 3012.9
## + gender:is_first_child                   1      67.6 78415 3012.9
## + gender:lunch_type                       1      31.1 78451 3013.2
## + gender:test_prep                        1      21.5 78461 3013.2
## + is_first_child:wkly_study_hours         2     272.3 78210 3013.3
## + gender:wkly_study_hours                 2     197.2 78285 3013.9
## + transport_means:wkly_study_hours        2     171.9 78311 3014.1
## + practice_sport:transport_means          2      92.0 78391 3014.7
## + practice_sport:is_first_child           2      53.0 78430 3015.0
## + ethnic_group:lunch_type                 4     533.7 77949 3015.4
## + ethnic_group:test_prep                  4     514.6 77968 3015.5
## + test_prep:parent_marital_status         3     224.0 78259 3015.7
## + gender:parent_marital_status            3     140.6 78342 3016.3
## + parent_educ:transport_means             5     664.5 77818 3016.4
## + lunch_type:parent_marital_status        3     128.4 78354 3016.4
## + gender:parent_educ                      5     587.5 77895 3017.0
## - parent_marital_status:wkly_study_hours  6    2395.3 80878 3017.1
## + parent_educ:lunch_type                  5     559.6 77923 3017.2
## + gender:ethnic_group                     4     256.9 78226 3017.5
## + ethnic_group:is_first_child             4     221.7 78261 3017.7
## - lunch_type:practice_sport               2    1393.9 79876 3017.8
## + parent_marital_status:practice_sport    6     467.3 78015 3019.9
## + parent_educ:test_prep                   5     194.3 78288 3019.9
## + parent_educ:practice_sport             10    1487.5 76995 3020.1
## + parent_educ:wkly_study_hours           10    1441.2 77041 3020.5
## - parent_marital_status:is_first_child    3    2065.7 80548 3020.7
## + ethnic_group:parent_marital_status     11    1648.0 76835 3020.9
## + ethnic_group:practice_sport             8     846.7 77636 3021.0
## + ethnic_group:wkly_study_hours           8     744.7 77738 3021.8
## + ethnic_group:parent_educ               20    2158.3 76324 3034.9
## - gender                                  1   12321.2 90804 3095.4
## 
## Step:  AIC=3011.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:parent_marital_status      15    4063.4 82808 3011.1
## <none>                                                78745 3011.4
## + lunch_type:test_prep                    1     262.1 78483 3011.4
## - lunch_type:wkly_study_hours             2     575.8 79321 3011.7
## + test_prep:practice_sport                2     468.3 78276 3011.8
## - parent_educ:is_first_child              5    1428.4 80173 3012.0
## - ethnic_group:transport_means            4    1168.4 79913 3012.1
## + lunch_type:transport_means              1     171.7 78573 3012.1
## + test_prep:wkly_study_hours              2     435.1 78310 3012.1
## + practice_sport:wkly_study_hours         4     949.3 77795 3012.2
## - parent_marital_status:transport_means   3     939.6 79684 3012.4
## + test_prep:is_first_child                1     129.3 78615 3012.4
## + test_prep:transport_means               1     121.3 78623 3012.5
## + gender:practice_sport                   2     386.6 78358 3012.5
## + is_first_child:transport_means          1     112.6 78632 3012.5
## + lunch_type:is_first_child               1     100.4 78644 3012.6
## + gender:is_first_child                   1      76.3 78668 3012.8
## + gender:transport_means                  1      74.0 78671 3012.8
## + gender:lunch_type                       1      46.0 78699 3013.0
## + is_first_child:wkly_study_hours         2     312.2 78432 3013.0
## + gender:test_prep                        1      29.1 78716 3013.2
## + gender:wkly_study_hours                 2     197.1 78548 3013.9
## + transport_means:wkly_study_hours        2     173.8 78571 3014.1
## + practice_sport:transport_means          2     114.1 78631 3014.5
## + practice_sport:is_first_child           2      62.2 78683 3014.9
## + ethnic_group:lunch_type                 4     561.7 78183 3015.1
## + ethnic_group:test_prep                  4     525.1 78220 3015.4
## + test_prep:parent_marital_status         3     228.3 78516 3015.7
## + parent_educ:transport_means             5     680.5 78064 3016.2
## + gender:parent_marital_status            3     140.2 78604 3016.3
## + lunch_type:parent_marital_status        3     119.1 78626 3016.5
## + gender:parent_educ                      5     618.2 78126 3016.7
## + parent_educ:lunch_type                  5     559.3 78185 3017.2
## - parent_marital_status:wkly_study_hours  6    2417.6 81162 3017.2
## + gender:ethnic_group                     4     269.6 78475 3017.3
## + ethnic_group:is_first_child             4     245.7 78499 3017.5
## - lunch_type:practice_sport               2    1369.3 80114 3017.5
## + parent_educ:practice_sport             10    1524.1 77221 3019.8
## + parent_educ:wkly_study_hours           10    1522.8 77222 3019.8
## + parent_marital_status:practice_sport    6     467.4 78277 3019.9
## + parent_educ:test_prep                   5     186.3 78558 3020.0
## + ethnic_group:practice_sport             8     913.7 77831 3020.5
## - parent_marital_status:is_first_child    3    2115.1 80860 3021.0
## + ethnic_group:wkly_study_hours           8     829.7 77915 3021.1
## + ethnic_group:parent_marital_status     11    1564.4 77180 3021.5
## + ethnic_group:parent_educ               20    2215.7 76529 3034.5
## - test_prep                               1    9863.4 88608 3079.0
## - gender                                  1   12254.8 91000 3094.7
## 
## Step:  AIC=3011.05
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:is_first_child + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:transport_means   3     657.5 83466 3009.7
## - parent_educ:is_first_child              5    1407.4 84216 3011.0
## <none>                                                82808 3011.1
## + parent_educ:parent_marital_status      15    4063.4 78745 3011.4
## + test_prep:transport_means               1     195.2 82613 3011.7
## + lunch_type:test_prep                    1     195.1 82613 3011.7
## + gender:practice_sport                   2     473.7 82334 3011.7
## + lunch_type:transport_means              1     185.2 82623 3011.7
## - ethnic_group:transport_means            4    1252.3 84060 3011.9
## + lunch_type:is_first_child               1     148.1 82660 3012.0
## + is_first_child:transport_means          1     126.7 82681 3012.2
## + test_prep:is_first_child                1     126.1 82682 3012.2
## + test_prep:wkly_study_hours              2     396.1 82412 3012.2
## - lunch_type:wkly_study_hours             2     731.3 83539 3012.2
## + test_prep:practice_sport                2     380.1 82428 3012.3
## + gender:is_first_child                   1      70.3 82738 3012.6
## + is_first_child:wkly_study_hours         2     345.7 82462 3012.6
## + practice_sport:wkly_study_hours         4     881.8 81926 3012.7
## + gender:transport_means                  1      38.6 82770 3012.8
## + gender:lunch_type                       1      36.2 82772 3012.8
## + gender:test_prep                        1      12.1 82796 3013.0
## + gender:wkly_study_hours                 2     277.5 82531 3013.1
## + transport_means:wkly_study_hours        2     155.0 82653 3013.9
## + practice_sport:transport_means          2      76.8 82731 3014.5
## + gender:parent_educ                      5     878.7 81929 3014.8
## + practice_sport:is_first_child           2      21.4 82787 3014.9
## - parent_marital_status:wkly_study_hours  6    2271.7 85080 3015.0
## - lunch_type:practice_sport               2    1129.5 83938 3015.1
## + lunch_type:parent_marital_status        3     198.0 82610 3015.6
## + ethnic_group:test_prep                  4     455.0 82353 3015.8
## + parent_educ:wkly_study_hours           10    2108.4 80700 3015.8
## - parent_marital_status:is_first_child    3    1546.8 84355 3016.0
## + test_prep:parent_marital_status         3     138.0 82670 3016.1
## + gender:parent_marital_status            3     117.4 82691 3016.2
## + parent_educ:transport_means             5     654.1 82154 3016.4
## + gender:ethnic_group                     4     364.0 82444 3016.4
## + ethnic_group:lunch_type                 4     347.8 82460 3016.6
## + ethnic_group:is_first_child             4     240.9 82567 3017.3
## + parent_educ:lunch_type                  5     513.6 82295 3017.4
## + parent_marital_status:practice_sport    6     744.7 82063 3017.7
## + parent_educ:practice_sport             10    1768.3 81040 3018.3
## + parent_educ:test_prep                   5     292.1 82516 3019.0
## + ethnic_group:practice_sport             8    1100.3 81708 3019.2
## + ethnic_group:parent_marital_status     11    1823.4 80985 3019.9
## + ethnic_group:wkly_study_hours           8     839.1 81969 3021.1
## + ethnic_group:parent_educ               20    2212.2 80596 3035.1
## - test_prep                               1    9566.9 92375 3073.6
## - gender                                  1   12656.8 95465 3093.0
## 
## Step:  AIC=3009.72
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:is_first_child + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:is_first_child              5    1301.6 84767 3008.8
## <none>                                                83466 3009.7
## - ethnic_group:transport_means            4    1174.0 84640 3010.0
## + test_prep:transport_means               1     229.8 83236 3010.1
## + is_first_child:transport_means          1     215.1 83251 3010.2
## + lunch_type:test_prep                    1     186.9 83279 3010.4
## + lunch_type:transport_means              1     186.6 83279 3010.4
## - lunch_type:wkly_study_hours             2     708.4 84174 3010.7
## + lunch_type:is_first_child               1     131.4 83334 3010.8
## + test_prep:is_first_child                1     127.4 83338 3010.8
## + gender:practice_sport                   2     407.4 83058 3010.8
## + gender:is_first_child                   1      96.5 83369 3011.0
## + parent_marital_status:transport_means   3     657.5 82808 3011.1
## + test_prep:wkly_study_hours              2     375.5 83090 3011.1
## + test_prep:practice_sport                2     375.2 83090 3011.1
## + gender:transport_means                  1      31.2 83435 3011.5
## + gender:lunch_type                       1      24.1 83442 3011.6
## + gender:test_prep                        1      17.3 83448 3011.6
## + practice_sport:wkly_study_hours         4     858.9 82607 3011.6
## + gender:wkly_study_hours                 2     280.1 83186 3011.7
## + is_first_child:wkly_study_hours         2     278.3 83187 3011.8
## + parent_educ:parent_marital_status      15    3781.3 79684 3012.4
## - parent_marital_status:wkly_study_hours  6    2151.2 85617 3012.7
## + transport_means:wkly_study_hours        2     134.1 83332 3012.8
## + gender:parent_educ                      5     969.9 82496 3012.8
## + practice_sport:transport_means          2     108.4 83357 3012.9
## + practice_sport:is_first_child           2       9.9 83456 3013.7
## + test_prep:parent_marital_status         3     220.3 83245 3014.2
## + parent_educ:wkly_study_hours           10    2160.5 81305 3014.2
## + lunch_type:parent_marital_status        3     191.9 83274 3014.4
## - lunch_type:practice_sport               2    1249.9 84716 3014.5
## + gender:parent_marital_status            3     129.0 83337 3014.8
## + gender:ethnic_group                     4     409.1 83057 3014.8
## + ethnic_group:test_prep                  4     400.2 83065 3014.9
## - parent_marital_status:is_first_child    3    1618.7 85084 3015.1
## + parent_educ:transport_means             5     613.7 82852 3015.4
## + ethnic_group:lunch_type                 4     331.8 83134 3015.4
## + parent_educ:lunch_type                  5     499.0 82967 3016.2
## + parent_educ:practice_sport             10    1891.8 81574 3016.2
## + ethnic_group:is_first_child             4     190.0 83276 3016.4
## + parent_marital_status:practice_sport    6     751.8 82714 3016.4
## + ethnic_group:practice_sport             8    1191.8 82274 3017.2
## + parent_educ:test_prep                   5     302.8 83163 3017.6
## + ethnic_group:parent_marital_status     11    1930.5 81535 3017.9
## + ethnic_group:wkly_study_hours           8     816.2 82649 3019.9
## + ethnic_group:parent_educ               20    2008.0 81458 3035.3
## - test_prep                               1    9947.6 93413 3074.2
## - gender                                  1   12642.9 96109 3090.9
## 
## Step:  AIC=3008.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## <none>                                                84767 3008.8
## + test_prep:transport_means               1     263.6 84504 3009.0
## + test_prep:practice_sport                2     543.3 84224 3009.1
## + is_first_child:transport_means          1     254.5 84513 3009.1
## - ethnic_group:transport_means            4    1232.7 86000 3009.4
## - lunch_type:wkly_study_hours             2     680.0 85447 3009.6
## + lunch_type:test_prep                    1     164.4 84603 3009.7
## + parent_educ:is_first_child              5    1301.6 83466 3009.7
## + lunch_type:transport_means              1     139.2 84628 3009.9
## + lunch_type:is_first_child               1     125.4 84642 3010.0
## + gender:practice_sport                   2     401.7 84366 3010.1
## + gender:is_first_child                   1     108.5 84659 3010.1
## + test_prep:wkly_study_hours              2     383.2 84384 3010.2
## + test_prep:is_first_child                1      63.8 84704 3010.4
## + gender:lunch_type                       1      22.9 84744 3010.7
## + gender:transport_means                  1      19.0 84748 3010.7
## + gender:test_prep                        1       5.3 84762 3010.8
## + parent_marital_status:transport_means   3     551.7 84216 3011.0
## - parent_marital_status:wkly_study_hours  6    2060.3 86828 3011.0
## + gender:wkly_study_hours                 2     232.3 84535 3011.2
## + is_first_child:wkly_study_hours         2     193.2 84574 3011.5
## + parent_educ:parent_marital_status      15    3818.8 80949 3011.7
## + transport_means:wkly_study_hours        2     107.3 84660 3012.1
## + practice_sport:transport_means          2     103.2 84664 3012.1
## + practice_sport:wkly_study_hours         4     671.8 84096 3012.2
## - parent_marital_status:is_first_child    3    1395.1 86162 3012.5
## + gender:parent_educ                      5     882.7 83885 3012.7
## + practice_sport:is_first_child           2       3.9 84763 3012.8
## + test_prep:parent_marital_status         3     189.7 84578 3013.5
## - lunch_type:practice_sport               2    1258.7 86026 3013.6
## + ethnic_group:test_prep                  4     470.3 84297 3013.6
## + lunch_type:parent_marital_status        3     184.0 84583 3013.6
## + gender:ethnic_group                     4     464.8 84303 3013.6
## + parent_educ:practice_sport             10    2151.4 82616 3013.7
## + ethnic_group:lunch_type                 4     388.3 84379 3014.1
## + gender:parent_marital_status            3      70.7 84697 3014.4
## + parent_educ:wkly_study_hours           10    2035.7 82732 3014.5
## + parent_educ:transport_means             5     615.3 84152 3014.6
## + parent_marital_status:practice_sport    6     773.3 83994 3015.4
## + parent_educ:lunch_type                  5     477.7 84290 3015.5
## + ethnic_group:is_first_child             4     188.4 84579 3015.5
## + parent_educ:test_prep                   5     338.3 84429 3016.5
## + ethnic_group:practice_sport             8    1107.8 83660 3017.1
## + ethnic_group:parent_marital_status     11    1856.5 82911 3017.8
## + ethnic_group:wkly_study_hours           8     765.8 84002 3019.5
## + ethnic_group:parent_educ               20    2002.1 82765 3034.8
## - parent_educ                             5    9294.5 94062 3060.2
## - test_prep                               1    9780.6 94548 3071.3
## - gender                                  1   12516.7 97284 3088.1
summary(stepwise_model_write)
## 
## Call:
## lm(formula = writing_score ~ gender + ethnic_group + parent_educ + 
##     lunch_type + test_prep + parent_marital_status + practice_sport + 
##     is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, 
##     data = df_4_mdl_write)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -48.763  -7.903   0.888   8.581  28.915 
## 
## Coefficients:
##                                                      Estimate Std. Error
## (Intercept)                                          67.70191    5.43878
## gendermale                                           -9.60342    1.06468
## ethnic_groupgroup B                                   2.66505    3.60266
## ethnic_groupgroup C                                   4.66371    3.29737
## ethnic_groupgroup D                                   6.89890    3.37504
## ethnic_groupgroup E                                  12.97757    3.72825
## parent_educbachelor's degree                          3.78448    1.87145
## parent_educhigh school                               -6.78406    1.62165
## parent_educmaster's degree                            5.13686    2.33681
## parent_educsome college                              -1.61594    1.62678
## parent_educsome high school                          -6.56468    1.63632
## lunch_typestandard                                    1.01145    3.66619
## test_prepnone                                        -8.81344    1.10535
## parent_marital_statusmarried                          7.41012    3.91977
## parent_marital_statussingle                          -3.99879    4.28335
## parent_marital_statuswidowed                         12.38775   10.44238
## practice_sportregularly                              -3.44862    3.11402
## practice_sportsometimes                              -5.25858    3.01623
## is_first_childyes                                     6.17523    3.24819
## transport_meansschool_bus                             5.99682    3.71242
## wkly_study_hours> 10                                -13.41677    4.87463
## wkly_study_hours10-May                               -1.32300    3.52689
## ethnic_groupgroup B:transport_meansschool_bus        -6.38307    4.47966
## ethnic_groupgroup C:transport_meansschool_bus        -7.47646    4.19267
## ethnic_groupgroup D:transport_meansschool_bus        -2.44868    4.26882
## ethnic_groupgroup E:transport_meansschool_bus       -10.30293    4.71351
## lunch_typestandard:practice_sportregularly            6.16137    3.77036
## lunch_typestandard:practice_sportsometimes           10.02195    3.67485
## lunch_typestandard:wkly_study_hours> 10               5.91877    3.33331
## lunch_typestandard:wkly_study_hours10-May            -0.07475    2.59512
## parent_marital_statusmarried:is_first_childyes       -7.62546    3.55928
## parent_marital_statussingle:is_first_childyes        -0.73567    3.95710
## parent_marital_statuswidowed:is_first_childyes       -5.74724    8.37846
## parent_marital_statusmarried:wkly_study_hours> 10    10.26572    4.74053
## parent_marital_statussingle:wkly_study_hours> 10     18.67985    5.30411
## parent_marital_statuswidowed:wkly_study_hours> 10     5.92668   13.84492
## parent_marital_statusmarried:wkly_study_hours10-May   3.32999    3.53309
## parent_marital_statussingle:wkly_study_hours10-May    8.29920    3.98905
## parent_marital_statuswidowed:wkly_study_hours10-May  -0.28438   10.39843
##                                                     t value Pr(>|t|)    
## (Intercept)                                          12.448  < 2e-16 ***
## gendermale                                           -9.020  < 2e-16 ***
## ethnic_groupgroup B                                   0.740 0.459770    
## ethnic_groupgroup C                                   1.414 0.157818    
## ethnic_groupgroup D                                   2.044 0.041419 *  
## ethnic_groupgroup E                                   3.481 0.000539 ***
## parent_educbachelor's degree                          2.022 0.043636 *  
## parent_educhigh school                               -4.183 3.34e-05 ***
## parent_educmaster's degree                            2.198 0.028347 *  
## parent_educsome college                              -0.993 0.320980    
## parent_educsome high school                          -4.012 6.86e-05 ***
## lunch_typestandard                                    0.276 0.782738    
## test_prepnone                                        -7.973 8.95e-15 ***
## parent_marital_statusmarried                          1.890 0.059222 .  
## parent_marital_statussingle                          -0.934 0.350937    
## parent_marital_statuswidowed                          1.186 0.236016    
## practice_sportregularly                              -1.107 0.268583    
## practice_sportsometimes                              -1.743 0.081816 .  
## is_first_childyes                                     1.901 0.057806 .  
## transport_meansschool_bus                             1.615 0.106809    
## wkly_study_hours> 10                                 -2.752 0.006112 ** 
## wkly_study_hours10-May                               -0.375 0.707718    
## ethnic_groupgroup B:transport_meansschool_bus        -1.425 0.154752    
## ethnic_groupgroup C:transport_meansschool_bus        -1.783 0.075100 .  
## ethnic_groupgroup D:transport_meansschool_bus        -0.574 0.566459    
## ethnic_groupgroup E:transport_meansschool_bus        -2.186 0.029248 *  
## lunch_typestandard:practice_sportregularly            1.634 0.102796    
## lunch_typestandard:practice_sportsometimes            2.727 0.006592 ** 
## lunch_typestandard:wkly_study_hours> 10               1.776 0.076344 .  
## lunch_typestandard:wkly_study_hours10-May            -0.029 0.977030    
## parent_marital_statusmarried:is_first_childyes       -2.142 0.032597 *  
## parent_marital_statussingle:is_first_childyes        -0.186 0.852583    
## parent_marital_statuswidowed:is_first_childyes       -0.686 0.493030    
## parent_marital_statusmarried:wkly_study_hours> 10     2.166 0.030776 *  
## parent_marital_statussingle:wkly_study_hours> 10      3.522 0.000464 ***
## parent_marital_statuswidowed:wkly_study_hours> 10     0.428 0.668763    
## parent_marital_statusmarried:wkly_study_hours10-May   0.943 0.346342    
## parent_marital_statussingle:wkly_study_hours10-May    2.080 0.037941 *  
## parent_marital_statuswidowed:wkly_study_hours10-May  -0.027 0.978192    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.4 on 551 degrees of freedom
## Multiple R-squared:  0.4032, Adjusted R-squared:  0.362 
## F-statistic: 9.796 on 38 and 551 DF,  p-value: < 2.2e-16

MAth Score

df_4_mdl_math=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,math_score)
full_fit_math=lm(math_score ~ .^2,data=df_4_mdl_math)
summary(full_fit_math)
## 
## Call:
## lm(formula = math_score ~ .^2, data = df_4_mdl_math)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.489  -7.390   0.168   7.221  24.154 
## 
## Coefficients: (4 not defined because of singularities)
##                                                            Estimate Std. Error
## (Intercept)                                                 68.0411    17.6110
## gendermale                                                   4.9827     8.9723
## ethnic_groupgroup B                                        -20.0944    15.1422
## ethnic_groupgroup C                                        -26.3767    14.2851
## ethnic_groupgroup D                                        -16.7609    15.5502
## ethnic_groupgroup E                                         -2.1592    14.5735
## parent_educbachelor's degree                                33.6079    15.9209
## parent_educhigh school                                      12.3061    13.1796
## parent_educmaster's degree                                 -25.1426    21.7572
## parent_educsome college                                     -3.3640    12.9319
## parent_educsome high school                                  1.5736    12.5441
## lunch_typestandard                                           2.2940     8.9077
## test_prepnone                                              -16.5825     9.2941
## parent_marital_statusmarried                                11.4586    11.8338
## parent_marital_statussingle                                  7.8399    14.2425
## parent_marital_statuswidowed                                56.5536    42.0759
## practice_sportregularly                                    -29.8202    14.1677
## practice_sportsometimes                                    -20.2458    14.0961
## is_first_childyes                                           13.1687    10.2054
## transport_meansschool_bus                                   -3.8403     9.0340
## wkly_study_hours> 10                                       -10.7976    13.9166
## wkly_study_hours10-May                                       4.6821    11.1838
## gendermale:ethnic_groupgroup B                               5.2886     5.6833
## gendermale:ethnic_groupgroup C                              10.1735     5.4655
## gendermale:ethnic_groupgroup D                               4.3097     5.4293
## gendermale:ethnic_groupgroup E                               6.3964     6.0199
## gendermale:parent_educbachelor's degree                     -4.5741     4.7806
## gendermale:parent_educhigh school                            1.1545     3.8987
## gendermale:parent_educmaster's degree                       11.0840     6.6935
## gendermale:parent_educsome college                          -4.4251     4.0942
## gendermale:parent_educsome high school                       1.5882     4.0216
## gendermale:lunch_typestandard                               -2.4581     2.7927
## gendermale:test_prepnone                                     0.3238     2.7833
## gendermale:parent_marital_statusmarried                     -2.2028     3.9676
## gendermale:parent_marital_statussingle                      -1.7229     4.4981
## gendermale:parent_marital_statuswidowed                     -1.1049    19.4773
## gendermale:practice_sportregularly                          -3.5415     4.7295
## gendermale:practice_sportsometimes                          -3.5726     4.7543
## gendermale:is_first_childyes                                 2.6976     2.9215
## gendermale:transport_meansschool_bus                        -0.3742     2.7006
## gendermale:wkly_study_hours> 10                             -3.4820     4.2367
## gendermale:wkly_study_hours10-May                           -1.9685     3.2131
## ethnic_groupgroup B:parent_educbachelor's degree            -4.2231    13.2581
## ethnic_groupgroup C:parent_educbachelor's degree            -3.7714    13.2368
## ethnic_groupgroup D:parent_educbachelor's degree            -1.2605    13.1369
## ethnic_groupgroup E:parent_educbachelor's degree            -9.8679    14.9506
## ethnic_groupgroup B:parent_educhigh school                 -12.1115     8.3005
## ethnic_groupgroup C:parent_educhigh school                  -7.8179     7.9780
## ethnic_groupgroup D:parent_educhigh school                  -4.1223     8.1111
## ethnic_groupgroup E:parent_educhigh school                  -7.1674     9.0331
## ethnic_groupgroup B:parent_educmaster's degree               6.1658    15.9289
## ethnic_groupgroup C:parent_educmaster's degree              -5.7091    14.7953
## ethnic_groupgroup D:parent_educmaster's degree               2.3388    15.0307
## ethnic_groupgroup E:parent_educmaster's degree              -0.8632    15.8151
## ethnic_groupgroup B:parent_educsome college                  2.3899     9.1796
## ethnic_groupgroup C:parent_educsome college                  3.2541     8.6646
## ethnic_groupgroup D:parent_educsome college                 12.0158     9.0246
## ethnic_groupgroup E:parent_educsome college                  1.8215     9.1236
## ethnic_groupgroup B:parent_educsome high school            -15.0749     8.7983
## ethnic_groupgroup C:parent_educsome high school             -4.9385     8.2551
## ethnic_groupgroup D:parent_educsome high school             -1.1085     8.3094
## ethnic_groupgroup E:parent_educsome high school              2.2394     8.9218
## ethnic_groupgroup B:lunch_typestandard                       3.7732     5.9098
## ethnic_groupgroup C:lunch_typestandard                       7.9926     5.7317
## ethnic_groupgroup D:lunch_typestandard                       4.4950     5.6419
## ethnic_groupgroup E:lunch_typestandard                       0.8425     6.5383
## ethnic_groupgroup B:test_prepnone                            2.4360     6.0294
## ethnic_groupgroup C:test_prepnone                            7.7889     5.6560
## ethnic_groupgroup D:test_prepnone                            7.7952     5.6674
## ethnic_groupgroup E:test_prepnone                           11.4896     6.1691
## ethnic_groupgroup B:parent_marital_statusmarried             4.5004     8.1401
## ethnic_groupgroup C:parent_marital_statusmarried             2.5638     7.4956
## ethnic_groupgroup D:parent_marital_statusmarried            -8.5771     7.3930
## ethnic_groupgroup E:parent_marital_statusmarried            -2.5010     8.1793
## ethnic_groupgroup B:parent_marital_statussingle             11.3279     9.6376
## ethnic_groupgroup C:parent_marital_statussingle              3.2686     9.1120
## ethnic_groupgroup D:parent_marital_statussingle             -2.3267     8.8048
## ethnic_groupgroup E:parent_marital_statussingle              6.0944    10.1485
## ethnic_groupgroup B:parent_marital_statuswidowed           112.2530   107.8327
## ethnic_groupgroup C:parent_marital_statuswidowed           143.7513    87.6384
## ethnic_groupgroup D:parent_marital_statuswidowed            31.6392    88.3465
## ethnic_groupgroup E:parent_marital_statuswidowed                 NA         NA
## ethnic_groupgroup B:practice_sportregularly                 18.1643    10.7978
## ethnic_groupgroup C:practice_sportregularly                 15.6305    10.7005
## ethnic_groupgroup D:practice_sportregularly                 15.7111    11.9445
## ethnic_groupgroup E:practice_sportregularly                 16.2136    10.9347
## ethnic_groupgroup B:practice_sportsometimes                 12.2733    11.5184
## ethnic_groupgroup C:practice_sportsometimes                 18.8952    11.2034
## ethnic_groupgroup D:practice_sportsometimes                 12.8401    12.3508
## ethnic_groupgroup E:practice_sportsometimes                 11.3892    11.2604
## ethnic_groupgroup B:is_first_childyes                       10.2091     5.9835
## ethnic_groupgroup C:is_first_childyes                       -0.1812     5.6444
## ethnic_groupgroup D:is_first_childyes                        1.1359     5.7099
## ethnic_groupgroup E:is_first_childyes                        3.4944     6.4312
## ethnic_groupgroup B:transport_meansschool_bus               -4.0964     5.9868
## ethnic_groupgroup C:transport_meansschool_bus              -10.1575     5.5281
## ethnic_groupgroup D:transport_meansschool_bus               -2.9759     5.5226
## ethnic_groupgroup E:transport_meansschool_bus              -11.7574     6.5192
## ethnic_groupgroup B:wkly_study_hours> 10                   -10.0294    10.1919
## ethnic_groupgroup C:wkly_study_hours> 10                     1.4113    10.0649
## ethnic_groupgroup D:wkly_study_hours> 10                     4.1762    10.0509
## ethnic_groupgroup E:wkly_study_hours> 10                    -3.4964    10.9491
## ethnic_groupgroup B:wkly_study_hours10-May                  -5.9718     8.5598
## ethnic_groupgroup C:wkly_study_hours10-May                   2.3955     8.3758
## ethnic_groupgroup D:wkly_study_hours10-May                   2.5625     8.5173
## ethnic_groupgroup E:wkly_study_hours10-May                  -2.6577     9.1705
## parent_educbachelor's degree:lunch_typestandard              2.1141     5.1441
## parent_educhigh school:lunch_typestandard                    0.3684     4.1512
## parent_educmaster's degree:lunch_typestandard                9.9274     7.6084
## parent_educsome college:lunch_typestandard                   3.3042     4.1848
## parent_educsome high school:lunch_typestandard               5.5345     4.3349
## parent_educbachelor's degree:test_prepnone                  -3.9833     4.7464
## parent_educhigh school:test_prepnone                        -1.1824     4.5458
## parent_educmaster's degree:test_prepnone                    -1.8200     8.0921
## parent_educsome college:test_prepnone                       -2.3529     4.2606
## parent_educsome high school:test_prepnone                    3.0111     4.1206
## parent_educbachelor's degree:parent_marital_statusmarried  -17.7590     8.4713
## parent_educhigh school:parent_marital_statusmarried          1.5718     5.9578
## parent_educmaster's degree:parent_marital_statusmarried      2.1560     8.6196
## parent_educsome college:parent_marital_statusmarried        -8.3928     5.8669
## parent_educsome high school:parent_marital_statusmarried    -7.8355     5.7817
## parent_educbachelor's degree:parent_marital_statussingle   -19.7203     9.1319
## parent_educhigh school:parent_marital_statussingle           3.9993     6.5081
## parent_educmaster's degree:parent_marital_statussingle      -1.7191     9.2012
## parent_educsome college:parent_marital_statussingle         -9.4469     6.5341
## parent_educsome high school:parent_marital_statussingle     -9.7176     6.4548
## parent_educbachelor's degree:parent_marital_statuswidowed  -38.7612    89.7785
## parent_educhigh school:parent_marital_statuswidowed       -117.8054    98.7809
## parent_educmaster's degree:parent_marital_statuswidowed   -110.3756    51.7457
## parent_educsome college:parent_marital_statuswidowed      -114.0106    64.8797
## parent_educsome high school:parent_marital_statuswidowed   -92.5395    77.7614
## parent_educbachelor's degree:practice_sportregularly        -3.7294     8.7461
## parent_educhigh school:practice_sportregularly             -13.6445     7.5268
## parent_educmaster's degree:practice_sportregularly           0.7016    10.6360
## parent_educsome college:practice_sportregularly             -0.2142     7.6542
## parent_educsome high school:practice_sportregularly         -2.7852     7.3917
## parent_educbachelor's degree:practice_sportsometimes       -12.4201     8.3926
## parent_educhigh school:practice_sportsometimes             -13.5033     7.1288
## parent_educmaster's degree:practice_sportsometimes           9.0615     8.8601
## parent_educsome college:practice_sportsometimes              1.2774     7.3663
## parent_educsome high school:practice_sportsometimes          0.4391     6.9262
## parent_educbachelor's degree:is_first_childyes               2.0649     5.1938
## parent_educhigh school:is_first_childyes                     8.6134     4.4335
## parent_educmaster's degree:is_first_childyes                 6.7664     7.7546
## parent_educsome college:is_first_childyes                    9.2132     4.3295
## parent_educsome high school:is_first_childyes                4.6542     4.3602
## parent_educbachelor's degree:transport_meansschool_bus       5.4304     5.1849
## parent_educhigh school:transport_meansschool_bus             4.0937     4.1394
## parent_educmaster's degree:transport_meansschool_bus        11.6831     6.3824
## parent_educsome college:transport_meansschool_bus            4.9041     4.2151
## parent_educsome high school:transport_meansschool_bus        6.9767     4.2890
## parent_educbachelor's degree:wkly_study_hours> 10          -14.7410     7.6498
## parent_educhigh school:wkly_study_hours> 10                -10.1303     6.3679
## parent_educmaster's degree:wkly_study_hours> 10              6.3671    13.7791
## parent_educsome college:wkly_study_hours> 10                -7.2539     6.4097
## parent_educsome high school:wkly_study_hours> 10           -11.3467     6.5283
## parent_educbachelor's degree:wkly_study_hours10-May         -3.4329     5.3169
## parent_educhigh school:wkly_study_hours10-May               -9.6586     4.9571
## parent_educmaster's degree:wkly_study_hours10-May            0.9849     7.0888
## parent_educsome college:wkly_study_hours10-May              -3.5554     5.0476
## parent_educsome high school:wkly_study_hours10-May         -10.4143     5.3257
## lunch_typestandard:test_prepnone                            -1.9452     3.1136
## lunch_typestandard:parent_marital_statusmarried             -6.2756     4.0742
## lunch_typestandard:parent_marital_statussingle              -2.2019     4.7175
## lunch_typestandard:parent_marital_statuswidowed            -21.8879    80.6364
## lunch_typestandard:practice_sportregularly                  10.3501     5.3704
## lunch_typestandard:practice_sportsometimes                  11.0341     5.1768
## lunch_typestandard:is_first_childyes                         0.1283     3.1548
## lunch_typestandard:transport_meansschool_bus                -2.5076     2.8951
## lunch_typestandard:wkly_study_hours> 10                      5.7376     4.4178
## lunch_typestandard:wkly_study_hours10-May                    0.5929     3.3046
## test_prepnone:parent_marital_statusmarried                   5.6467     4.1442
## test_prepnone:parent_marital_statussingle                    2.5438     4.7712
## test_prepnone:parent_marital_statuswidowed                 -70.1691    42.1289
## test_prepnone:practice_sportregularly                        1.5825     5.1802
## test_prepnone:practice_sportsometimes                        3.1630     5.0767
## test_prepnone:is_first_childyes                             -0.6723     3.1267
## test_prepnone:transport_meansschool_bus                      0.4150     2.8429
## test_prepnone:wkly_study_hours> 10                          -4.6995     4.4626
## test_prepnone:wkly_study_hours10-May                         1.6772     3.5219
## parent_marital_statusmarried:practice_sportregularly         9.1006     6.6592
## parent_marital_statussingle:practice_sportregularly          2.6152     8.7085
## parent_marital_statuswidowed:practice_sportregularly        22.5587    85.2725
## parent_marital_statusmarried:practice_sportsometimes         5.1124     6.5673
## parent_marital_statussingle:practice_sportsometimes         -1.6116     8.5136
## parent_marital_statuswidowed:practice_sportsometimes             NA         NA
## parent_marital_statusmarried:is_first_childyes             -12.7542     4.8986
## parent_marital_statussingle:is_first_childyes               -4.9445     5.4292
## parent_marital_statuswidowed:is_first_childyes              47.8196    30.2193
## parent_marital_statusmarried:transport_meansschool_bus       4.6203     4.0454
## parent_marital_statussingle:transport_meansschool_bus       -2.0235     4.6103
## parent_marital_statuswidowed:transport_meansschool_bus     -34.0699    19.6388
## parent_marital_statusmarried:wkly_study_hours> 10           18.1048     6.3197
## parent_marital_statussingle:wkly_study_hours> 10            21.8022     7.0282
## parent_marital_statuswidowed:wkly_study_hours> 10                NA         NA
## parent_marital_statusmarried:wkly_study_hours10-May          1.2179     4.6394
## parent_marital_statussingle:wkly_study_hours10-May           3.3543     5.1241
## parent_marital_statuswidowed:wkly_study_hours10-May              NA         NA
## practice_sportregularly:is_first_childyes                   -3.3085     6.0157
## practice_sportsometimes:is_first_childyes                   -5.4272     5.8699
## practice_sportregularly:transport_meansschool_bus            9.9774     5.0267
## practice_sportsometimes:transport_meansschool_bus            5.9885     4.8789
## practice_sportregularly:wkly_study_hours> 10                 2.6252     7.1266
## practice_sportsometimes:wkly_study_hours> 10                 2.0680     6.9901
## practice_sportregularly:wkly_study_hours10-May               7.8713     5.4844
## practice_sportsometimes:wkly_study_hours10-May               2.5781     5.4074
## is_first_childyes:transport_meansschool_bus                 -5.3887     3.0599
## is_first_childyes:wkly_study_hours> 10                       2.8322     4.6001
## is_first_childyes:wkly_study_hours10-May                    -4.9634     3.4724
## transport_meansschool_bus:wkly_study_hours> 10               4.0303     4.4205
## transport_meansschool_bus:wkly_study_hours10-May             2.7910     3.1920
##                                                           t value Pr(>|t|)    
## (Intercept)                                                 3.864 0.000131 ***
## gendermale                                                  0.555 0.578989    
## ethnic_groupgroup B                                        -1.327 0.185283    
## ethnic_groupgroup C                                        -1.846 0.065599 .  
## ethnic_groupgroup D                                        -1.078 0.281775    
## ethnic_groupgroup E                                        -0.148 0.882295    
## parent_educbachelor's degree                                2.111 0.035426 *  
## parent_educhigh school                                      0.934 0.351036    
## parent_educmaster's degree                                 -1.156 0.248565    
## parent_educsome college                                    -0.260 0.794902    
## parent_educsome high school                                 0.125 0.900238    
## lunch_typestandard                                          0.258 0.796904    
## test_prepnone                                              -1.784 0.075183 .  
## parent_marital_statusmarried                                0.968 0.333510    
## parent_marital_statussingle                                 0.550 0.582326    
## parent_marital_statuswidowed                                1.344 0.179717    
## practice_sportregularly                                    -2.105 0.035959 *  
## practice_sportsometimes                                    -1.436 0.151741    
## is_first_childyes                                           1.290 0.197701    
## transport_meansschool_bus                                  -0.425 0.671008    
## wkly_study_hours> 10                                       -0.776 0.438299    
## wkly_study_hours10-May                                      0.419 0.675703    
## gendermale:ethnic_groupgroup B                              0.931 0.352678    
## gendermale:ethnic_groupgroup C                              1.861 0.063454 .  
## gendermale:ethnic_groupgroup D                              0.794 0.427811    
## gendermale:ethnic_groupgroup E                              1.063 0.288659    
## gendermale:parent_educbachelor's degree                    -0.957 0.339269    
## gendermale:parent_educhigh school                           0.296 0.767289    
## gendermale:parent_educmaster's degree                       1.656 0.098552 .  
## gendermale:parent_educsome college                         -1.081 0.280453    
## gendermale:parent_educsome high school                      0.395 0.693115    
## gendermale:lunch_typestandard                              -0.880 0.379317    
## gendermale:test_prepnone                                    0.116 0.907448    
## gendermale:parent_marital_statusmarried                    -0.555 0.579095    
## gendermale:parent_marital_statussingle                     -0.383 0.701904    
## gendermale:parent_marital_statuswidowed                    -0.057 0.954790    
## gendermale:practice_sportregularly                         -0.749 0.454437    
## gendermale:practice_sportsometimes                         -0.751 0.452841    
## gendermale:is_first_childyes                                0.923 0.356397    
## gendermale:transport_meansschool_bus                       -0.139 0.889859    
## gendermale:wkly_study_hours> 10                            -0.822 0.411658    
## gendermale:wkly_study_hours10-May                          -0.613 0.540476    
## ethnic_groupgroup B:parent_educbachelor's degree           -0.319 0.750255    
## ethnic_groupgroup C:parent_educbachelor's degree           -0.285 0.775863    
## ethnic_groupgroup D:parent_educbachelor's degree           -0.096 0.923607    
## ethnic_groupgroup E:parent_educbachelor's degree           -0.660 0.509629    
## ethnic_groupgroup B:parent_educhigh school                 -1.459 0.145350    
## ethnic_groupgroup C:parent_educhigh school                 -0.980 0.327741    
## ethnic_groupgroup D:parent_educhigh school                 -0.508 0.611582    
## ethnic_groupgroup E:parent_educhigh school                 -0.793 0.428002    
## ethnic_groupgroup B:parent_educmaster's degree              0.387 0.698911    
## ethnic_groupgroup C:parent_educmaster's degree             -0.386 0.699808    
## ethnic_groupgroup D:parent_educmaster's degree              0.156 0.876431    
## ethnic_groupgroup E:parent_educmaster's degree             -0.055 0.956503    
## ethnic_groupgroup B:parent_educsome college                 0.260 0.794732    
## ethnic_groupgroup C:parent_educsome college                 0.376 0.707455    
## ethnic_groupgroup D:parent_educsome college                 1.331 0.183836    
## ethnic_groupgroup E:parent_educsome college                 0.200 0.841866    
## ethnic_groupgroup B:parent_educsome high school            -1.713 0.087450 .  
## ethnic_groupgroup C:parent_educsome high school            -0.598 0.550037    
## ethnic_groupgroup D:parent_educsome high school            -0.133 0.893944    
## ethnic_groupgroup E:parent_educsome high school             0.251 0.801944    
## ethnic_groupgroup B:lunch_typestandard                      0.638 0.523555    
## ethnic_groupgroup C:lunch_typestandard                      1.394 0.163987    
## ethnic_groupgroup D:lunch_typestandard                      0.797 0.426112    
## ethnic_groupgroup E:lunch_typestandard                      0.129 0.897536    
## ethnic_groupgroup B:test_prepnone                           0.404 0.686423    
## ethnic_groupgroup C:test_prepnone                           1.377 0.169289    
## ethnic_groupgroup D:test_prepnone                           1.375 0.169796    
## ethnic_groupgroup E:test_prepnone                           1.862 0.063307 .  
## ethnic_groupgroup B:parent_marital_statusmarried            0.553 0.580679    
## ethnic_groupgroup C:parent_marital_statusmarried            0.342 0.732511    
## ethnic_groupgroup D:parent_marital_statusmarried           -1.160 0.246704    
## ethnic_groupgroup E:parent_marital_statusmarried           -0.306 0.759941    
## ethnic_groupgroup B:parent_marital_statussingle             1.175 0.240572    
## ethnic_groupgroup C:parent_marital_statussingle             0.359 0.720004    
## ethnic_groupgroup D:parent_marital_statussingle            -0.264 0.791728    
## ethnic_groupgroup E:parent_marital_statussingle             0.601 0.548513    
## ethnic_groupgroup B:parent_marital_statuswidowed            1.041 0.298536    
## ethnic_groupgroup C:parent_marital_statuswidowed            1.640 0.101768    
## ethnic_groupgroup D:parent_marital_statuswidowed            0.358 0.720446    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                 1.682 0.093341 .  
## ethnic_groupgroup C:practice_sportregularly                 1.461 0.144908    
## ethnic_groupgroup D:practice_sportregularly                 1.315 0.189183    
## ethnic_groupgroup E:practice_sportregularly                 1.483 0.138959    
## ethnic_groupgroup B:practice_sportsometimes                 1.066 0.287304    
## ethnic_groupgroup C:practice_sportsometimes                 1.687 0.092504 .  
## ethnic_groupgroup D:practice_sportsometimes                 1.040 0.299174    
## ethnic_groupgroup E:practice_sportsometimes                 1.011 0.312443    
## ethnic_groupgroup B:is_first_childyes                       1.706 0.088779 .  
## ethnic_groupgroup C:is_first_childyes                      -0.032 0.974411    
## ethnic_groupgroup D:is_first_childyes                       0.199 0.842418    
## ethnic_groupgroup E:is_first_childyes                       0.543 0.587200    
## ethnic_groupgroup B:transport_meansschool_bus              -0.684 0.494241    
## ethnic_groupgroup C:transport_meansschool_bus              -1.837 0.066921 .  
## ethnic_groupgroup D:transport_meansschool_bus              -0.539 0.590297    
## ethnic_groupgroup E:transport_meansschool_bus              -1.804 0.072093 .  
## ethnic_groupgroup B:wkly_study_hours> 10                   -0.984 0.325710    
## ethnic_groupgroup C:wkly_study_hours> 10                    0.140 0.888562    
## ethnic_groupgroup D:wkly_study_hours> 10                    0.416 0.678007    
## ethnic_groupgroup E:wkly_study_hours> 10                   -0.319 0.749646    
## ethnic_groupgroup B:wkly_study_hours10-May                 -0.698 0.485813    
## ethnic_groupgroup C:wkly_study_hours10-May                  0.286 0.775035    
## ethnic_groupgroup D:wkly_study_hours10-May                  0.301 0.763685    
## ethnic_groupgroup E:wkly_study_hours10-May                 -0.290 0.772121    
## parent_educbachelor's degree:lunch_typestandard             0.411 0.681330    
## parent_educhigh school:lunch_typestandard                   0.089 0.929339    
## parent_educmaster's degree:lunch_typestandard               1.305 0.192749    
## parent_educsome college:lunch_typestandard                  0.790 0.430256    
## parent_educsome high school:lunch_typestandard              1.277 0.202472    
## parent_educbachelor's degree:test_prepnone                 -0.839 0.401869    
## parent_educhigh school:test_prepnone                       -0.260 0.794920    
## parent_educmaster's degree:test_prepnone                   -0.225 0.822173    
## parent_educsome college:test_prepnone                      -0.552 0.581102    
## parent_educsome high school:test_prepnone                   0.731 0.465380    
## parent_educbachelor's degree:parent_marital_statusmarried  -2.096 0.036705 *  
## parent_educhigh school:parent_marital_statusmarried         0.264 0.792052    
## parent_educmaster's degree:parent_marital_statusmarried     0.250 0.802627    
## parent_educsome college:parent_marital_statusmarried       -1.431 0.153379    
## parent_educsome high school:parent_marital_statusmarried   -1.355 0.176143    
## parent_educbachelor's degree:parent_marital_statussingle   -2.160 0.031431 *  
## parent_educhigh school:parent_marital_statussingle          0.615 0.539246    
## parent_educmaster's degree:parent_marital_statussingle     -0.187 0.851886    
## parent_educsome college:parent_marital_statussingle        -1.446 0.149058    
## parent_educsome high school:parent_marital_statussingle    -1.505 0.133023    
## parent_educbachelor's degree:parent_marital_statuswidowed  -0.432 0.666171    
## parent_educhigh school:parent_marital_statuswidowed        -1.193 0.233767    
## parent_educmaster's degree:parent_marital_statuswidowed    -2.133 0.033557 *  
## parent_educsome college:parent_marital_statuswidowed       -1.757 0.079672 .  
## parent_educsome high school:parent_marital_statuswidowed   -1.190 0.234766    
## parent_educbachelor's degree:practice_sportregularly       -0.426 0.670053    
## parent_educhigh school:practice_sportregularly             -1.813 0.070647 .  
## parent_educmaster's degree:practice_sportregularly          0.066 0.947437    
## parent_educsome college:practice_sportregularly            -0.028 0.977692    
## parent_educsome high school:practice_sportregularly        -0.377 0.706532    
## parent_educbachelor's degree:practice_sportsometimes       -1.480 0.139724    
## parent_educhigh school:practice_sportsometimes             -1.894 0.058951 .  
## parent_educmaster's degree:practice_sportsometimes          1.023 0.307081    
## parent_educsome college:practice_sportsometimes             0.173 0.862420    
## parent_educsome high school:practice_sportsometimes         0.063 0.949489    
## parent_educbachelor's degree:is_first_childyes              0.398 0.691162    
## parent_educhigh school:is_first_childyes                    1.943 0.052773 .  
## parent_educmaster's degree:is_first_childyes                0.873 0.383445    
## parent_educsome college:is_first_childyes                   2.128 0.033972 *  
## parent_educsome high school:is_first_childyes               1.067 0.286450    
## parent_educbachelor's degree:transport_meansschool_bus      1.047 0.295600    
## parent_educhigh school:transport_meansschool_bus            0.989 0.323307    
## parent_educmaster's degree:transport_meansschool_bus        1.831 0.067950 .  
## parent_educsome college:transport_meansschool_bus           1.163 0.245371    
## parent_educsome high school:transport_meansschool_bus       1.627 0.104635    
## parent_educbachelor's degree:wkly_study_hours> 10          -1.927 0.054721 .  
## parent_educhigh school:wkly_study_hours> 10                -1.591 0.112471    
## parent_educmaster's degree:wkly_study_hours> 10             0.462 0.644281    
## parent_educsome college:wkly_study_hours> 10               -1.132 0.258463    
## parent_educsome high school:wkly_study_hours> 10           -1.738 0.083002 .  
## parent_educbachelor's degree:wkly_study_hours10-May        -0.646 0.518891    
## parent_educhigh school:wkly_study_hours10-May              -1.948 0.052093 .  
## parent_educmaster's degree:wkly_study_hours10-May           0.139 0.889578    
## parent_educsome college:wkly_study_hours10-May             -0.704 0.481637    
## parent_educsome high school:wkly_study_hours10-May         -1.955 0.051251 .  
## lunch_typestandard:test_prepnone                           -0.625 0.532521    
## lunch_typestandard:parent_marital_statusmarried            -1.540 0.124305    
## lunch_typestandard:parent_marital_statussingle             -0.467 0.640946    
## lunch_typestandard:parent_marital_statuswidowed            -0.271 0.786200    
## lunch_typestandard:practice_sportregularly                  1.927 0.054686 .  
## lunch_typestandard:practice_sportsometimes                  2.131 0.033689 *  
## lunch_typestandard:is_first_childyes                        0.041 0.967588    
## lunch_typestandard:transport_meansschool_bus               -0.866 0.386933    
## lunch_typestandard:wkly_study_hours> 10                     1.299 0.194815    
## lunch_typestandard:wkly_study_hours10-May                   0.179 0.857717    
## test_prepnone:parent_marital_statusmarried                  1.363 0.173819    
## test_prepnone:parent_marital_statussingle                   0.533 0.594231    
## test_prepnone:parent_marital_statuswidowed                 -1.666 0.096615 .  
## test_prepnone:practice_sportregularly                       0.305 0.760155    
## test_prepnone:practice_sportsometimes                       0.623 0.533633    
## test_prepnone:is_first_childyes                            -0.215 0.829855    
## test_prepnone:transport_meansschool_bus                     0.146 0.884028    
## test_prepnone:wkly_study_hours> 10                         -1.053 0.292966    
## test_prepnone:wkly_study_hours10-May                        0.476 0.634185    
## parent_marital_statusmarried:practice_sportregularly        1.367 0.172546    
## parent_marital_statussingle:practice_sportregularly         0.300 0.764107    
## parent_marital_statuswidowed:practice_sportregularly        0.265 0.791500    
## parent_marital_statusmarried:practice_sportsometimes        0.778 0.436770    
## parent_marital_statussingle:practice_sportsometimes        -0.189 0.849955    
## parent_marital_statuswidowed:practice_sportsometimes           NA       NA    
## parent_marital_statusmarried:is_first_childyes             -2.604 0.009583 ** 
## parent_marital_statussingle:is_first_childyes              -0.911 0.363014    
## parent_marital_statuswidowed:is_first_childyes              1.582 0.114379    
## parent_marital_statusmarried:transport_meansschool_bus      1.142 0.254126    
## parent_marital_statussingle:transport_meansschool_bus      -0.439 0.660982    
## parent_marital_statuswidowed:transport_meansschool_bus     -1.735 0.083576 .  
## parent_marital_statusmarried:wkly_study_hours> 10           2.865 0.004403 ** 
## parent_marital_statussingle:wkly_study_hours> 10            3.102 0.002064 ** 
## parent_marital_statuswidowed:wkly_study_hours> 10              NA       NA    
## parent_marital_statusmarried:wkly_study_hours10-May         0.263 0.793062    
## parent_marital_statussingle:wkly_study_hours10-May          0.655 0.513103    
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## practice_sportregularly:is_first_childyes                  -0.550 0.582650    
## practice_sportsometimes:is_first_childyes                  -0.925 0.355759    
## practice_sportregularly:transport_meansschool_bus           1.985 0.047872 *  
## practice_sportsometimes:transport_meansschool_bus           1.227 0.220411    
## practice_sportregularly:wkly_study_hours> 10                0.368 0.712800    
## practice_sportsometimes:wkly_study_hours> 10                0.296 0.767511    
## practice_sportregularly:wkly_study_hours10-May              1.435 0.152043    
## practice_sportsometimes:wkly_study_hours10-May              0.477 0.633796    
## is_first_childyes:transport_meansschool_bus                -1.761 0.079028 .  
## is_first_childyes:wkly_study_hours> 10                      0.616 0.538468    
## is_first_childyes:wkly_study_hours10-May                   -1.429 0.153714    
## transport_meansschool_bus:wkly_study_hours> 10              0.912 0.362481    
## transport_meansschool_bus:wkly_study_hours10-May            0.874 0.382459    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.21 on 383 degrees of freedom
## Multiple R-squared:  0.5635, Adjusted R-squared:  0.3287 
## F-statistic:   2.4 on 206 and 383 DF,  p-value: 7.833e-14
stepwise_model_math <- step(full_fit_math, direction = "both", trace = 1)
## Start:  AIC=3204.25
## math_score ~ (gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours)^2
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_educ               20    3316.3 70110 3192.8
## - parent_educ:test_prep                   5     440.1 67234 3198.1
## - gender:parent_marital_status            3      54.0 66847 3198.7
## - parent_educ:lunch_type                  5     591.2 67385 3199.4
## - ethnic_group:wkly_study_hours           8    1323.8 68117 3199.8
## - parent_educ:wkly_study_hours           10    1801.1 68595 3199.9
## - test_prep:practice_sport                2      93.5 66887 3201.1
## - parent_marital_status:practice_sport    4     550.9 67344 3201.1
## - gender:practice_sport                   2     107.4 66901 3201.2
## - gender:wkly_study_hours                 2     123.6 66917 3201.3
## - parent_educ:transport_means             5     809.3 67603 3201.4
## - ethnic_group:lunch_type                 4     591.0 67384 3201.4
## - transport_means:wkly_study_hours        2     187.6 66981 3201.9
## - practice_sport:is_first_child           2     198.4 66992 3202.0
## - lunch_type:is_first_child               1       0.3 66794 3202.3
## - gender:test_prep                        1       2.4 66796 3202.3
## - gender:transport_means                  1       3.3 66797 3202.3
## - test_prep:transport_means               1       3.7 66797 3202.3
## - test_prep:is_first_child                1       8.1 66802 3202.3
## - practice_sport:wkly_study_hours         4     718.0 67511 3202.6
## - lunch_type:test_prep                    1      68.1 66862 3202.9
## - ethnic_group:practice_sport             8    1701.9 68495 3203.1
## - lunch_type:wkly_study_hours             2     352.3 67146 3203.4
## - lunch_type:transport_means              1     130.8 66924 3203.4
## - gender:lunch_type                       1     135.1 66929 3203.4
## - gender:is_first_child                   1     148.7 66942 3203.6
## - test_prep:parent_marital_status         2     403.4 67197 3203.8
## - gender:ethnic_group                     4     869.6 67663 3203.9
## - parent_educ:is_first_child              5    1132.1 67926 3204.2
## <none>                                                66793 3204.3
## - gender:parent_educ                      5    1173.5 67967 3204.5
## - test_prep:wkly_study_hours              2     516.4 67310 3204.8
## - ethnic_group:parent_marital_status      9    2150.3 68944 3204.9
## - lunch_type:parent_marital_status        2     552.7 67346 3205.1
## - ethnic_group:test_prep                  4    1027.0 67820 3205.3
## - parent_educ:practice_sport             10    2545.2 69339 3206.3
## - ethnic_group:is_first_child             4    1194.4 67988 3206.7
## - parent_educ:parent_marital_status      13    3334.3 70128 3207.0
## - is_first_child:transport_means          1     540.9 67334 3207.0
## - practice_sport:transport_means          2     773.2 67567 3207.0
## - is_first_child:wkly_study_hours         2     781.2 67575 3207.1
## - lunch_type:practice_sport               2     806.9 67600 3207.3
## - ethnic_group:transport_means            4    1369.9 68163 3208.2
## - parent_marital_status:transport_means   3    1399.6 68193 3210.5
## - parent_marital_status:wkly_study_hours  4    2104.0 68897 3214.5
## - parent_marital_status:is_first_child    2    1736.9 68530 3215.4
## 
## Step:  AIC=3192.84
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:wkly_study_hours           10    1343.3 71453 3184.0
## - ethnic_group:wkly_study_hours           8     963.6 71073 3184.9
## - parent_educ:test_prep                   5     338.0 70448 3185.7
## - parent_educ:lunch_type                  5     451.8 70562 3186.6
## - gender:parent_marital_status            3      77.7 70187 3187.5
## - ethnic_group:practice_sport             8    1396.5 71506 3188.5
## - parent_marital_status:practice_sport    4     526.1 70636 3189.3
## - gender:wkly_study_hours                 2      84.8 70194 3189.6
## - test_prep:practice_sport                2      90.5 70200 3189.6
## - parent_educ:transport_means             5     905.7 71015 3190.4
## - practice_sport:is_first_child           2     203.1 70313 3190.5
## - ethnic_group:lunch_type                 4     690.5 70800 3190.6
## - gender:practice_sport                   2     238.2 70348 3190.8
## - lunch_type:is_first_child               1       0.2 70110 3190.8
## - gender:transport_means                  1       0.2 70110 3190.8
## - lunch_type:test_prep                    1       1.0 70111 3190.8
## - gender:test_prep                        1       6.0 70116 3190.9
## - test_prep:transport_means               1      13.7 70123 3191.0
## - gender:is_first_child                   1      26.2 70136 3191.1
## - test_prep:is_first_child                1      33.4 70143 3191.1
## - lunch_type:parent_marital_status        2     291.9 70402 3191.3
## - gender:lunch_type                       1     114.9 70225 3191.8
## - ethnic_group:test_prep                  4     836.4 70946 3191.8
## - transport_means:wkly_study_hours        2     360.6 70470 3191.9
## - practice_sport:wkly_study_hours         4     853.3 70963 3192.0
## - parent_educ:is_first_child              5    1098.4 71208 3192.0
## - gender:ethnic_group                     4     860.5 70970 3192.0
## - test_prep:parent_marital_status         2     402.3 70512 3192.2
## - gender:parent_educ                      5    1125.5 71235 3192.2
## - lunch_type:transport_means              1     226.0 70336 3192.7
## <none>                                                70110 3192.8
## - lunch_type:wkly_study_hours             2     538.0 70648 3193.3
## - is_first_child:wkly_study_hours         2     543.0 70653 3193.4
## - test_prep:wkly_study_hours              2     569.9 70680 3193.6
## - ethnic_group:parent_marital_status      9    2293.6 72403 3193.8
## - parent_educ:practice_sport             10    2568.4 72678 3194.1
## - is_first_child:transport_means          1     470.4 70580 3194.8
## - practice_sport:transport_means          2     724.0 70834 3194.9
## - lunch_type:practice_sport               2     860.0 70970 3196.0
## - ethnic_group:transport_means            4    1409.3 71519 3196.6
## - parent_marital_status:transport_means   3    1169.4 71279 3196.6
## - ethnic_group:is_first_child             4    1483.9 71594 3197.2
## - parent_marital_status:wkly_study_hours  4    1669.0 71779 3198.7
## - parent_educ:parent_marital_status      13    3948.0 74058 3199.2
## - parent_marital_status:is_first_child    2    1642.9 71753 3202.5
## + ethnic_group:parent_educ               20    3316.3 66793 3204.3
## 
## Step:  AIC=3184.04
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:wkly_study_hours           8    1060.7 72514 3176.7
## - parent_educ:lunch_type                  5     330.0 71783 3176.8
## - parent_educ:test_prep                   5     395.5 71848 3177.3
## - gender:parent_marital_status            3      71.4 71524 3178.6
## - ethnic_group:practice_sport             8    1299.7 72753 3178.7
## - ethnic_group:lunch_type                 4     543.5 71997 3180.5
## - parent_marital_status:practice_sport    4     607.7 72061 3181.0
## - test_prep:practice_sport                2     164.8 71618 3181.4
## - gender:wkly_study_hours                 2     178.6 71632 3181.5
## - gender:practice_sport                   2     193.6 71647 3181.6
## - practice_sport:is_first_child           2     204.1 71657 3181.7
## - parent_educ:transport_means             5     939.1 72392 3181.7
## - practice_sport:wkly_study_hours         4     701.9 72155 3181.8
## - lunch_type:test_prep                    1       0.1 71453 3182.0
## - gender:transport_means                  1       2.0 71455 3182.1
## - lunch_type:is_first_child               1       7.3 71460 3182.1
## - gender:test_prep                        1       9.7 71463 3182.1
## - ethnic_group:test_prep                  4     740.2 72193 3182.1
## - test_prep:is_first_child                1      16.6 71470 3182.2
## - test_prep:transport_means               1      16.8 71470 3182.2
## - gender:is_first_child                   1      23.1 71476 3182.2
## - lunch_type:parent_marital_status        2     307.7 71761 3182.6
## - lunch_type:wkly_study_hours             2     327.7 71781 3182.7
## - gender:lunch_type                       1      94.3 71547 3182.8
## - gender:parent_educ                      5    1100.3 72553 3183.1
## - transport_means:wkly_study_hours        2     407.0 71860 3183.4
## - parent_educ:is_first_child              5    1144.4 72597 3183.4
## - is_first_child:wkly_study_hours         2     417.3 71870 3183.5
## - gender:ethnic_group                     4     920.2 72373 3183.6
## - test_prep:parent_marital_status         2     440.7 71894 3183.7
## <none>                                                71453 3184.0
## - lunch_type:transport_means              1     318.5 71772 3184.7
## - practice_sport:transport_means          2     638.5 72091 3185.3
## - is_first_child:transport_means          1     494.4 71947 3186.1
## - ethnic_group:parent_marital_status      9    2511.3 73964 3186.4
## - ethnic_group:transport_means            4    1268.3 72721 3186.4
## - lunch_type:practice_sport               2     795.8 72249 3186.6
## - test_prep:wkly_study_hours              2     800.9 72254 3186.6
## - parent_educ:practice_sport             10    2798.9 74252 3186.7
## - parent_marital_status:transport_means   3    1242.1 72695 3188.2
## - ethnic_group:is_first_child             4    1585.3 73038 3189.0
## - parent_marital_status:wkly_study_hours  4    1707.0 73160 3190.0
## - parent_educ:parent_marital_status      13    4246.1 75699 3192.1
## + parent_educ:wkly_study_hours           10    1343.3 70110 3192.8
## - parent_marital_status:is_first_child    2    1880.9 73334 3195.4
## + ethnic_group:parent_educ               20    2858.5 68595 3199.9
## 
## Step:  AIC=3176.73
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:lunch_type                  5     294.6 72808 3169.1
## - parent_educ:test_prep                   5     425.1 72939 3170.2
## - gender:parent_marital_status            3      77.7 72591 3171.4
## - ethnic_group:practice_sport             8    1324.8 73838 3171.4
## - parent_marital_status:practice_sport    4     477.7 72991 3172.6
## - ethnic_group:lunch_type                 4     592.3 73106 3173.5
## - parent_educ:transport_means             5     852.7 73366 3173.6
## - gender:wkly_study_hours                 2     138.0 72652 3173.9
## - test_prep:practice_sport                2     157.5 72671 3174.0
## - ethnic_group:test_prep                  4     699.6 73213 3174.4
## - gender:practice_sport                   2     212.8 72726 3174.5
## - practice_sport:wkly_study_hours         4     715.7 73229 3174.5
## - practice_sport:is_first_child           2     230.8 72744 3174.6
## - lunch_type:test_prep                    1       3.8 72518 3174.8
## - gender:transport_means                  1       3.8 72518 3174.8
## - transport_means:wkly_study_hours        2     251.7 72765 3174.8
## - gender:is_first_child                   1       9.8 72523 3174.8
## - lunch_type:is_first_child               1      10.0 72524 3174.8
## - test_prep:transport_means               1      14.0 72528 3174.8
## - gender:test_prep                        1      32.5 72546 3175.0
## - test_prep:is_first_child                1      49.0 72563 3175.1
## - gender:parent_educ                      5    1062.9 73577 3175.3
## - lunch_type:parent_marital_status        2     327.1 72841 3175.4
## - gender:lunch_type                       1     100.0 72614 3175.5
## - lunch_type:wkly_study_hours             2     408.7 72922 3176.0
## - gender:ethnic_group                     4     915.4 73429 3176.1
## - parent_educ:is_first_child              5    1198.1 73712 3176.4
## <none>                                                72514 3176.7
## - test_prep:parent_marital_status         2     499.2 73013 3176.8
## - is_first_child:wkly_study_hours         2     516.9 73031 3176.9
## - lunch_type:transport_means              1     292.6 72806 3177.1
## - ethnic_group:parent_marital_status      9    2400.6 74914 3177.9
## - practice_sport:transport_means          2     658.8 73173 3178.1
## - ethnic_group:transport_means            4    1211.0 73725 3178.5
## - parent_educ:practice_sport             10    2730.9 75245 3178.5
## - is_first_child:transport_means          1     494.6 73008 3178.7
## - test_prep:wkly_study_hours              2     797.9 73312 3179.2
## - lunch_type:practice_sport               2     872.4 73386 3179.8
## - parent_marital_status:transport_means   3    1276.5 73790 3181.0
## - parent_marital_status:wkly_study_hours  4    1550.3 74064 3181.2
## - ethnic_group:is_first_child             4    1638.0 74152 3181.9
## - parent_educ:parent_marital_status      13    4105.1 76619 3183.2
## + ethnic_group:wkly_study_hours           8    1060.7 71453 3184.0
## + parent_educ:wkly_study_hours           10    1440.4 71073 3184.9
## - parent_marital_status:is_first_child    2    1784.1 74298 3187.1
## + ethnic_group:parent_educ               20    2546.0 69968 3195.6
## 
## Step:  AIC=3169.12
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:test_prep                   5     359.4 73168 3162.0
## - ethnic_group:practice_sport             8    1287.1 74095 3163.5
## - gender:parent_marital_status            3      84.3 72893 3163.8
## - parent_marital_status:practice_sport    4     510.3 73319 3165.2
## - ethnic_group:lunch_type                 4     611.1 73419 3166.1
## - gender:wkly_study_hours                 2     132.3 72941 3166.2
## - test_prep:practice_sport                2     157.8 72966 3166.4
## - parent_educ:transport_means             5     914.4 73723 3166.5
## - ethnic_group:test_prep                  4     686.0 73494 3166.7
## - gender:practice_sport                   2     217.7 73026 3166.9
## - practice_sport:is_first_child           2     246.8 73055 3167.1
## - gender:transport_means                  1       1.0 72809 3167.1
## - lunch_type:test_prep                    1       1.8 72810 3167.1
## - test_prep:transport_means               1      14.7 72823 3167.2
## - lunch_type:is_first_child               1      14.9 72823 3167.2
## - practice_sport:wkly_study_hours         4     759.8 73568 3167.2
## - transport_means:wkly_study_hours        2     270.4 73079 3167.3
## - gender:is_first_child                   1      30.9 72839 3167.4
## - gender:test_prep                        1      38.9 72847 3167.4
## - test_prep:is_first_child                1      39.2 72847 3167.4
## - gender:parent_educ                      5    1056.1 73864 3167.6
## - lunch_type:parent_marital_status        2     329.5 73138 3167.8
## - lunch_type:wkly_study_hours             2     370.3 73179 3168.1
## - gender:lunch_type                       1     140.8 72949 3168.3
## - gender:ethnic_group                     4     914.4 73723 3168.5
## - parent_educ:is_first_child              5    1171.9 73980 3168.5
## <none>                                                72808 3169.1
## - test_prep:parent_marital_status         2     532.2 73340 3169.4
## - lunch_type:transport_means              1     287.4 73096 3169.4
## - is_first_child:wkly_study_hours         2     545.4 73354 3169.5
## - ethnic_group:parent_marital_status      9    2363.0 75171 3170.0
## - ethnic_group:transport_means            4    1190.2 73998 3170.7
## - practice_sport:transport_means          2     751.2 73559 3171.2
## - is_first_child:transport_means          1     510.9 73319 3171.2
## - test_prep:wkly_study_hours              2     786.4 73595 3171.5
## - lunch_type:practice_sport               2     835.6 73644 3171.9
## - parent_educ:practice_sport             10    2882.8 75691 3172.0
## - parent_marital_status:transport_means   3    1345.6 74154 3173.9
## - ethnic_group:is_first_child             4    1656.4 74465 3174.4
## - parent_marital_status:wkly_study_hours  4    1675.9 74484 3174.5
## - parent_educ:parent_marital_status      13    4184.5 76993 3176.1
## + parent_educ:lunch_type                  5     294.6 72514 3176.7
## + ethnic_group:wkly_study_hours           8    1025.2 71783 3176.8
## + parent_educ:wkly_study_hours           10    1298.6 71510 3178.5
## - parent_marital_status:is_first_child    2    1962.0 74770 3180.8
## + ethnic_group:parent_educ               20    2526.6 70282 3188.3
## 
## Step:  AIC=3162.03
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:practice_sport             8    1278.6 74446 3156.2
## - gender:parent_marital_status            3      87.6 73255 3156.7
## - parent_marital_status:practice_sport    4     490.9 73659 3158.0
## - ethnic_group:test_prep                  4     630.4 73798 3159.1
## - test_prep:practice_sport                2     132.4 73300 3159.1
## - gender:wkly_study_hours                 2     150.1 73318 3159.2
## - ethnic_group:lunch_type                 4     667.4 73835 3159.4
## - parent_educ:transport_means             5     964.9 74132 3159.8
## - gender:practice_sport                   2     214.9 73382 3159.8
## - gender:transport_means                  1       0.1 73168 3160.0
## - gender:parent_educ                      5    1000.6 74168 3160.0
## - practice_sport:wkly_study_hours         4     751.8 73919 3160.1
## - lunch_type:test_prep                    1       7.1 73175 3160.1
## - test_prep:transport_means               1      12.8 73180 3160.1
## - transport_means:wkly_study_hours        2     262.3 73430 3160.1
## - lunch_type:is_first_child               1      24.2 73192 3160.2
## - gender:is_first_child                   1      25.1 73193 3160.2
## - practice_sport:is_first_child           2     277.1 73445 3160.3
## - test_prep:is_first_child                1      46.8 73214 3160.4
## - gender:test_prep                        1      47.0 73215 3160.4
## - lunch_type:parent_marital_status        2     304.2 73472 3160.5
## - gender:lunch_type                       1     121.5 73289 3161.0
## - lunch_type:wkly_study_hours             2     410.5 73578 3161.3
## - gender:ethnic_group                     4     912.8 74080 3161.3
## - parent_educ:is_first_child              5    1196.4 74364 3161.6
## - is_first_child:wkly_study_hours         2     486.7 73654 3161.9
## <none>                                                73168 3162.0
## - lunch_type:transport_means              1     256.3 73424 3162.1
## - test_prep:parent_marital_status         2     519.3 73687 3162.2
## - ethnic_group:parent_marital_status      9    2307.6 75475 3162.3
## - ethnic_group:transport_means            4    1145.8 74313 3163.2
## - practice_sport:transport_means          2     780.1 73948 3164.3
## - parent_educ:practice_sport             10    2851.5 76019 3164.6
## - is_first_child:transport_means          1     590.4 73758 3164.8
## - test_prep:wkly_study_hours              2     856.9 74024 3164.9
## - lunch_type:practice_sport               2     894.2 74062 3165.2
## - parent_marital_status:transport_means   3    1347.2 74515 3166.8
## - parent_marital_status:wkly_study_hours  4    1749.0 74917 3168.0
## - ethnic_group:is_first_child             4    1750.8 74918 3168.0
## - parent_educ:parent_marital_status      13    4071.8 77239 3168.0
## + parent_educ:test_prep                   5     359.4 72808 3169.1
## + ethnic_group:wkly_study_hours           8    1054.8 72113 3169.5
## + parent_educ:lunch_type                  5     228.9 72939 3170.2
## + parent_educ:wkly_study_hours           10    1351.3 71816 3171.0
## - parent_marital_status:is_first_child    2    2006.6 75174 3174.0
## + ethnic_group:parent_educ               20    2379.5 70788 3182.5
## 
## Step:  AIC=3156.25
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_marital_status            3      67.0 74513 3150.8
## - parent_educ:transport_means             5     841.7 75288 3152.9
## - test_prep:practice_sport                2     106.9 74553 3153.1
## - ethnic_group:test_prep                  4     620.2 75066 3153.1
## - gender:parent_educ                      5     928.1 75374 3153.6
## - parent_marital_status:practice_sport    4     715.9 75162 3153.9
## - gender:ethnic_group                     4     740.0 75186 3154.1
## - practice_sport:is_first_child           2     233.2 74679 3154.1
## - gender:wkly_study_hours                 2     239.5 74686 3154.1
## - ethnic_group:lunch_type                 4     753.4 75200 3154.2
## - practice_sport:wkly_study_hours         4     757.6 75204 3154.2
## - gender:transport_means                  1       0.0 74446 3154.2
## - gender:is_first_child                   1       4.0 74450 3154.3
## - lunch_type:is_first_child               1       6.3 74452 3154.3
## - test_prep:transport_means               1      14.3 74461 3154.4
## - gender:test_prep                        1      27.0 74473 3154.5
## - test_prep:is_first_child                1      36.1 74482 3154.5
## - lunch_type:test_prep                    1      40.4 74487 3154.6
## - transport_means:wkly_study_hours        2     312.2 74758 3154.7
## - lunch_type:parent_marital_status        2     336.7 74783 3154.9
## - gender:lunch_type                       1      91.8 74538 3155.0
## - gender:practice_sport                   2     372.3 74818 3155.2
## - lunch_type:wkly_study_hours             2     438.7 74885 3155.7
## - lunch_type:transport_means              1     207.5 74654 3155.9
## <none>                                                74446 3156.2
## - is_first_child:wkly_study_hours         2     513.1 74959 3156.3
## - test_prep:parent_marital_status         2     564.5 75011 3156.7
## - ethnic_group:parent_marital_status      9    2399.2 76845 3157.0
## - parent_educ:is_first_child              5    1373.5 75820 3157.0
## - test_prep:wkly_study_hours              2     686.9 75133 3157.7
## - ethnic_group:transport_means            4    1209.0 75655 3157.8
## - practice_sport:transport_means          2     767.5 75214 3158.3
## - lunch_type:practice_sport               2     901.2 75347 3159.3
## - parent_educ:practice_sport             10    2985.5 77432 3159.4
## - is_first_child:transport_means          1     699.2 75145 3159.8
## - ethnic_group:is_first_child             4    1570.1 76016 3160.6
## - parent_educ:parent_marital_status      13    4000.5 78447 3161.1
## - parent_marital_status:transport_means   3    1482.2 75928 3161.9
## + ethnic_group:practice_sport             8    1278.6 73168 3162.0
## - parent_marital_status:wkly_study_hours  4    1838.7 76285 3162.6
## + parent_educ:test_prep                   5     350.9 74095 3163.5
## + ethnic_group:wkly_study_hours           8    1066.6 73380 3163.7
## + parent_educ:lunch_type                  5     190.6 74256 3164.7
## + parent_educ:wkly_study_hours           10    1298.4 73148 3165.9
## - parent_marital_status:is_first_child    2    1757.2 76203 3166.0
## + ethnic_group:parent_educ               20    2053.9 72392 3179.7
## 
## Step:  AIC=3150.78
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:transport_means             5     837.2 75350 3147.4
## - test_prep:practice_sport                2     123.5 74637 3147.8
## - ethnic_group:test_prep                  4     647.9 75161 3147.9
## - gender:parent_educ                      5     953.7 75467 3148.3
## - parent_marital_status:practice_sport    4     707.6 75221 3148.4
## - gender:ethnic_group                     4     713.3 75227 3148.4
## - practice_sport:is_first_child           2     226.7 74740 3148.6
## - gender:transport_means                  1       0.1 74513 3148.8
## - ethnic_group:lunch_type                 4     763.7 75277 3148.8
## - lunch_type:is_first_child               1       5.5 74519 3148.8
## - gender:wkly_study_hours                 2     259.9 74773 3148.8
## - gender:is_first_child                   1       7.7 74521 3148.8
## - test_prep:transport_means               1      13.5 74527 3148.9
## - practice_sport:wkly_study_hours         4     781.9 75295 3148.9
## - gender:test_prep                        1      30.2 74543 3149.0
## - test_prep:is_first_child                1      37.1 74550 3149.1
## - lunch_type:test_prep                    1      38.2 74551 3149.1
## - transport_means:wkly_study_hours        2     313.8 74827 3149.3
## - gender:lunch_type                       1      86.4 74600 3149.5
## - lunch_type:parent_marital_status        2     372.7 74886 3149.7
## - gender:practice_sport                   2     398.1 74911 3149.9
## - lunch_type:wkly_study_hours             2     465.2 74978 3150.5
## - lunch_type:transport_means              1     219.7 74733 3150.5
## - is_first_child:wkly_study_hours         2     502.1 75015 3150.7
## <none>                                                74513 3150.8
## - test_prep:parent_marital_status         2     572.4 75086 3151.3
## - parent_educ:is_first_child              5    1383.9 75897 3151.6
## - test_prep:wkly_study_hours              2     682.1 75195 3152.2
## - ethnic_group:transport_means            4    1201.4 75715 3152.2
## - practice_sport:transport_means          2     757.6 75271 3152.7
## - ethnic_group:parent_marital_status      9    2645.4 77159 3153.4
## - lunch_type:practice_sport               2     979.2 75492 3154.5
## - parent_educ:practice_sport             10    3086.3 77599 3154.7
## - is_first_child:transport_means          1     756.1 75269 3154.7
## - ethnic_group:is_first_child             4    1552.8 76066 3154.9
## - parent_educ:parent_marital_status      13    3992.8 78506 3155.6
## + gender:parent_marital_status            3      67.0 74446 3156.2
## + ethnic_group:practice_sport             8    1258.0 73255 3156.7
## - parent_marital_status:wkly_study_hours  4    1820.1 76333 3157.0
## - parent_marital_status:transport_means   3    1677.8 76191 3157.9
## + parent_educ:test_prep                   5     353.8 74159 3158.0
## + ethnic_group:wkly_study_hours           8    1069.4 73444 3158.3
## + parent_educ:lunch_type                  5     197.6 74316 3159.2
## + parent_educ:wkly_study_hours           10    1285.8 73227 3160.5
## - parent_marital_status:is_first_child    2    1819.2 76332 3161.0
## + ethnic_group:parent_educ               20    2094.0 72419 3174.0
## 
## Step:  AIC=3147.37
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:ethnic_group                     4     625.0 75975 3144.2
## - parent_marital_status:practice_sport    4     639.9 75990 3144.4
## - test_prep:practice_sport                2     137.2 75488 3144.4
## - practice_sport:is_first_child           2     183.7 75534 3144.8
## - ethnic_group:test_prep                  4     699.4 76050 3144.8
## - gender:parent_educ                      5     964.7 76315 3144.9
## - gender:wkly_study_hours                 2     223.3 75574 3145.1
## - gender:transport_means                  1       0.0 75350 3145.4
## - lunch_type:is_first_child               1       3.2 75354 3145.4
## - gender:is_first_child                   1       3.4 75354 3145.4
## - test_prep:transport_means               1      18.3 75369 3145.5
## - gender:test_prep                        1      25.6 75376 3145.6
## - transport_means:wkly_study_hours        2     288.2 75639 3145.6
## - lunch_type:test_prep                    1      45.2 75396 3145.7
## - test_prep:is_first_child                1      70.8 75421 3145.9
## - practice_sport:wkly_study_hours         4     851.2 76202 3146.0
## - gender:lunch_type                       1     110.4 75461 3146.2
## - ethnic_group:lunch_type                 4     903.0 76253 3146.4
## - lunch_type:parent_marital_status        2     449.3 75800 3146.9
## - is_first_child:wkly_study_hours         2     475.6 75826 3147.1
## - lunch_type:transport_means              1     226.7 75577 3147.1
## - gender:practice_sport                   2     488.4 75839 3147.2
## <none>                                                75350 3147.4
## - test_prep:parent_marital_status         2     561.5 75912 3147.8
## - lunch_type:wkly_study_hours             2     588.6 75939 3148.0
## - practice_sport:transport_means          2     593.3 75944 3148.0
## - parent_educ:is_first_child              5    1426.3 76777 3148.4
## - test_prep:wkly_study_hours              2     674.7 76025 3148.6
## - ethnic_group:transport_means            4    1321.3 76672 3149.6
## - ethnic_group:parent_marital_status      9    2697.0 78047 3150.1
## - parent_educ:practice_sport             10    3037.1 78388 3150.7
## - is_first_child:transport_means          1     689.2 76040 3150.7
## + parent_educ:transport_means             5     837.2 74513 3150.8
## - ethnic_group:is_first_child             4    1647.5 76998 3152.1
## - lunch_type:practice_sport               2    1148.9 76499 3152.3
## - parent_educ:parent_marital_status      13    4056.5 79407 3152.3
## + gender:parent_marital_status            3      62.5 75288 3152.9
## - parent_marital_status:transport_means   3    1562.5 76913 3153.5
## - parent_marital_status:wkly_study_hours  4    1918.6 77269 3154.2
## + parent_educ:test_prep                   5     390.5 74960 3154.3
## + ethnic_group:practice_sport             8    1138.4 74212 3154.4
## + parent_educ:lunch_type                  5     246.2 75104 3155.4
## + ethnic_group:wkly_study_hours           8     977.8 74373 3155.7
## - parent_marital_status:is_first_child    2    1802.2 77153 3157.3
## + parent_educ:wkly_study_hours           10    1256.7 74094 3157.4
## + ethnic_group:parent_educ               20    2385.2 72965 3168.4
## 
## Step:  AIC=3144.24
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:parent_educ + 
##     gender:lunch_type + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_educ                      5     803.3 76779 3140.5
## - ethnic_group:test_prep                  4     583.4 76559 3140.8
## - parent_marital_status:practice_sport    4     607.7 76583 3140.9
## - test_prep:practice_sport                2     130.4 76106 3141.3
## - practice_sport:is_first_child           2     230.6 76206 3142.0
## - gender:transport_means                  1       2.2 75978 3142.3
## - lunch_type:is_first_child               1       2.4 75978 3142.3
## - gender:is_first_child                   1       8.7 75984 3142.3
## - gender:test_prep                        1      14.5 75990 3142.4
## - test_prep:transport_means               1      15.5 75991 3142.4
## - gender:wkly_study_hours                 2     283.2 76259 3142.4
## - lunch_type:test_prep                    1      62.2 76038 3142.7
## - transport_means:wkly_study_hours        2     331.5 76307 3142.8
## - test_prep:is_first_child                1      78.2 76054 3142.9
## - gender:lunch_type                       1      98.6 76074 3143.0
## - practice_sport:wkly_study_hours         4     895.9 76871 3143.2
## - ethnic_group:lunch_type                 4     898.8 76874 3143.2
## - lunch_type:parent_marital_status        2     387.7 76363 3143.2
## - is_first_child:wkly_study_hours         2     485.3 76461 3144.0
## - lunch_type:transport_means              1     230.9 76206 3144.0
## - gender:practice_sport                   2     505.5 76481 3144.2
## <none>                                                75975 3144.2
## - test_prep:parent_marital_status         2     573.9 76549 3144.7
## - lunch_type:wkly_study_hours             2     580.0 76555 3144.7
## - practice_sport:transport_means          2     587.3 76563 3144.8
## - test_prep:wkly_study_hours              2     723.8 76699 3145.8
## - ethnic_group:parent_marital_status      9    2606.7 78582 3146.1
## - ethnic_group:transport_means            4    1335.3 77311 3146.5
## - parent_educ:is_first_child              5    1638.2 77614 3146.8
## + gender:ethnic_group                     4     625.0 75350 3147.4
## - parent_educ:practice_sport             10    3044.3 79020 3147.4
## - is_first_child:transport_means          1     745.1 76720 3148.0
## + parent_educ:transport_means             5     748.8 75227 3148.4
## - ethnic_group:is_first_child             4    1618.4 77594 3148.7
## - parent_educ:parent_marital_status      13    4147.5 80123 3149.6
## + gender:parent_marital_status            3      53.1 75922 3149.8
## - parent_marital_status:wkly_study_hours  4    1869.3 77845 3150.6
## - lunch_type:practice_sport               2    1362.2 77338 3150.7
## - parent_marital_status:transport_means   3    1625.8 77601 3150.7
## + parent_educ:test_prep                   5     378.4 75597 3151.3
## + parent_educ:lunch_type                  5     249.3 75726 3152.3
## + ethnic_group:practice_sport             8     990.4 74985 3152.5
## + ethnic_group:wkly_study_hours           8     951.0 75024 3152.8
## + parent_educ:wkly_study_hours           10    1276.1 74699 3154.3
## - parent_marital_status:is_first_child    2    1937.3 77913 3155.1
## + ethnic_group:parent_educ               20    2426.2 73549 3165.1
## 
## Step:  AIC=3140.45
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:test_prep                  4     579.8 77359 3136.9
## - parent_marital_status:practice_sport    4     610.1 77389 3137.1
## - test_prep:practice_sport                2     174.1 76953 3137.8
## - gender:transport_means                  1       2.3 76781 3138.5
## - lunch_type:is_first_child               1       3.9 76783 3138.5
## - gender:is_first_child                   1       8.2 76787 3138.5
## - ethnic_group:lunch_type                 4     793.2 77572 3138.5
## - test_prep:transport_means               1       8.6 76787 3138.5
## - practice_sport:is_first_child           2     271.5 77050 3138.5
## - gender:test_prep                        1      13.6 76792 3138.6
## - gender:wkly_study_hours                 2     305.8 77084 3138.8
## - transport_means:wkly_study_hours        2     333.7 77112 3139.0
## - practice_sport:wkly_study_hours         4     866.5 77645 3139.1
## - lunch_type:test_prep                    1      89.9 76869 3139.1
## - lunch_type:parent_marital_status        2     356.6 77135 3139.2
## - gender:lunch_type                       1     106.1 76885 3139.3
## - test_prep:is_first_child                1     121.6 76900 3139.4
## - gender:practice_sport                   2     513.8 77292 3140.4
## <none>                                                76779 3140.4
## - test_prep:parent_marital_status         2     543.9 77323 3140.6
## - is_first_child:wkly_study_hours         2     547.5 77326 3140.6
## - practice_sport:transport_means          2     576.1 77355 3140.9
## - lunch_type:transport_means              1     337.5 77116 3141.0
## - lunch_type:wkly_study_hours             2     602.4 77381 3141.1
## - ethnic_group:parent_marital_status      9    2495.1 79274 3141.3
## - parent_educ:is_first_child              5    1473.0 78252 3141.7
## - test_prep:wkly_study_hours              2     793.8 77573 3142.5
## - parent_educ:practice_sport             10    2997.2 79776 3143.0
## - ethnic_group:transport_means            4    1487.1 78266 3143.8
## - is_first_child:transport_means          1     729.0 77508 3144.0
## + gender:parent_educ                      5     803.3 75975 3144.2
## - ethnic_group:is_first_child             4    1574.1 78353 3144.4
## + parent_educ:transport_means             5     771.5 76007 3144.5
## + gender:ethnic_group                     4     463.6 76315 3144.9
## + gender:parent_marital_status            3      49.7 76729 3146.1
## - lunch_type:practice_sport               2    1378.5 78157 3146.9
## - parent_marital_status:wkly_study_hours  4    1932.2 78711 3147.1
## - parent_marital_status:transport_means   3    1712.3 78491 3147.5
## + parent_educ:test_prep                   5     325.1 76454 3147.9
## + parent_educ:lunch_type                  5     253.8 76525 3148.5
## - parent_educ:parent_marital_status      13    4591.9 81371 3148.7
## + ethnic_group:practice_sport             8     953.6 75825 3149.1
## + ethnic_group:wkly_study_hours           8     934.0 75845 3149.2
## + parent_educ:wkly_study_hours           10    1262.9 75516 3150.7
## - parent_marital_status:is_first_child    2    1915.9 78695 3151.0
## + ethnic_group:parent_educ               20    2444.2 74335 3161.4
## 
## Step:  AIC=3136.89
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:practice_sport    4     533.2 77892 3132.9
## - test_prep:practice_sport                2     161.1 77520 3134.1
## - ethnic_group:lunch_type                 4     747.4 78106 3134.6
## - gender:transport_means                  1       1.4 77360 3134.9
## - gender:is_first_child                   1       3.8 77362 3134.9
## - lunch_type:is_first_child               1       8.7 77367 3135.0
## - gender:test_prep                        1      10.2 77369 3135.0
## - test_prep:transport_means               1      11.0 77370 3135.0
## - gender:wkly_study_hours                 2     274.9 77633 3135.0
## - practice_sport:is_first_child           2     307.1 77666 3135.2
## - practice_sport:wkly_study_hours         4     846.0 78204 3135.3
## - transport_means:wkly_study_hours        2     321.1 77680 3135.3
## - lunch_type:test_prep                    1      90.8 77449 3135.6
## - lunch_type:parent_marital_status        2     359.1 77718 3135.6
## - gender:lunch_type                       1      96.6 77455 3135.6
## - test_prep:is_first_child                1     102.3 77461 3135.7
## - test_prep:parent_marital_status         2     465.8 77824 3136.4
## - gender:practice_sport                   2     500.6 77859 3136.7
## - is_first_child:wkly_study_hours         2     507.8 77866 3136.8
## <none>                                                77359 3136.9
## - ethnic_group:parent_marital_status      9    2421.8 79780 3137.1
## - practice_sport:transport_means          2     583.7 77942 3137.3
## - lunch_type:transport_means              1     352.8 77711 3137.6
## - lunch_type:wkly_study_hours             2     639.5 77998 3137.8
## - parent_educ:is_first_child              5    1498.7 78857 3138.2
## - parent_educ:practice_sport             10    3002.3 80361 3139.3
## - test_prep:wkly_study_hours              2     860.1 78219 3139.4
## - is_first_child:transport_means          1     727.5 78086 3140.4
## + ethnic_group:test_prep                  4     579.8 76779 3140.4
## + parent_educ:transport_means             5     819.8 76539 3140.6
## + gender:parent_educ                      5     799.7 76559 3140.8
## - ethnic_group:is_first_child             4    1599.6 78958 3141.0
## - ethnic_group:transport_means            4    1611.9 78970 3141.1
## + gender:ethnic_group                     4     374.8 76984 3142.0
## + gender:parent_marital_status            3      72.6 77286 3142.3
## - parent_marital_status:wkly_study_hours  4    1929.3 79288 3143.4
## - lunch_type:practice_sport               2    1417.0 78776 3143.6
## - parent_marital_status:transport_means   3    1711.0 79070 3143.8
## + parent_educ:test_prep                   5     315.5 77043 3144.5
## + parent_educ:lunch_type                  5     243.5 77115 3145.0
## - parent_educ:parent_marital_status      13    4692.5 82051 3145.6
## + ethnic_group:practice_sport             8     942.1 76416 3145.7
## + ethnic_group:wkly_study_hours           8     878.6 76480 3146.2
## + parent_educ:wkly_study_hours           10    1190.6 76168 3147.7
## - parent_marital_status:is_first_child    2    2031.7 79390 3148.2
## + ethnic_group:parent_educ               20    2464.6 74894 3157.8
## 
## Step:  AIC=3132.94
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:parent_marital_status        3     368.2 78260 3129.7
## - test_prep:practice_sport                2     150.3 78042 3130.1
## - ethnic_group:lunch_type                 4     775.5 78667 3130.8
## - practice_sport:is_first_child           2     265.2 78157 3130.9
## - gender:is_first_child                   1       1.6 77893 3130.9
## - gender:transport_means                  1       3.6 77895 3131.0
## - test_prep:transport_means               1       9.1 77901 3131.0
## - lunch_type:is_first_child               1      14.4 77906 3131.1
## - gender:test_prep                        1      22.0 77914 3131.1
## - gender:wkly_study_hours                 2     316.5 78208 3131.3
## - transport_means:wkly_study_hours        2     323.4 78215 3131.4
## - ethnic_group:parent_marital_status     10    2477.6 80369 3131.4
## - practice_sport:wkly_study_hours         4     878.9 78771 3131.6
## - test_prep:is_first_child                1      96.0 77988 3131.7
## - lunch_type:test_prep                    1     100.7 77992 3131.7
## - gender:lunch_type                       1     110.2 78002 3131.8
## - test_prep:parent_marital_status         2     413.7 78305 3132.1
## - is_first_child:wkly_study_hours         2     514.9 78407 3132.8
## - gender:practice_sport                   2     523.4 78415 3132.9
## <none>                                                77892 3132.9
## - practice_sport:transport_means          2     544.8 78437 3133.1
## - lunch_type:transport_means              1     315.9 78208 3133.3
## - lunch_type:wkly_study_hours             2     646.8 78539 3133.8
## - parent_educ:is_first_child              5    1450.7 79342 3133.8
## - parent_educ:practice_sport             10    2867.2 80759 3134.3
## - ethnic_group:transport_means            4    1416.9 79309 3135.6
## - test_prep:wkly_study_hours              2     963.4 78855 3136.2
## - is_first_child:transport_means          1     722.5 78614 3136.4
## + parent_marital_status:practice_sport    4     533.2 77359 3136.9
## + gender:parent_educ                      5     794.5 77097 3136.9
## - ethnic_group:is_first_child             4    1601.7 79493 3136.9
## + parent_educ:transport_means             5     772.0 77120 3137.1
## + ethnic_group:test_prep                  4     502.9 77389 3137.1
## - parent_marital_status:wkly_study_hours  5    1966.9 79859 3137.7
## + gender:ethnic_group                     4     347.9 77544 3138.3
## + gender:parent_marital_status            3      64.2 77828 3138.5
## - parent_marital_status:transport_means   3    1696.1 79588 3139.7
## - lunch_type:practice_sport               2    1453.7 79345 3139.8
## + parent_educ:test_prep                   5     317.5 77574 3140.5
## + ethnic_group:practice_sport             8    1088.4 76803 3140.6
## + parent_educ:lunch_type                  5     251.8 77640 3141.0
## + ethnic_group:wkly_study_hours           8     797.6 77094 3142.9
## - parent_educ:parent_marital_status      14    5190.5 83082 3143.0
## + parent_educ:wkly_study_hours           10    1174.0 76718 3144.0
## - parent_marital_status:is_first_child    2    2196.3 80088 3145.3
## + ethnic_group:parent_educ               20    2483.8 75408 3153.8
## 
## Step:  AIC=3129.72
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:practice_sport                2     165.1 78425 3127.0
## - practice_sport:is_first_child           2     212.2 78472 3127.3
## - ethnic_group:lunch_type                 4     777.4 79037 3127.6
## - gender:is_first_child                   1       4.9 78265 3127.8
## - gender:wkly_study_hours                 2     271.6 78532 3127.8
## - gender:transport_means                  1       6.8 78267 3127.8
## - test_prep:transport_means               1      10.2 78270 3127.8
## - ethnic_group:parent_marital_status     10    2435.5 80696 3127.8
## - lunch_type:is_first_child               1      18.4 78278 3127.9
## - practice_sport:wkly_study_hours         4     826.1 79086 3127.9
## - gender:test_prep                        1      38.7 78299 3128.0
## - lunch_type:test_prep                    1      84.5 78345 3128.4
## - test_prep:is_first_child                1      94.7 78355 3128.4
## - transport_means:wkly_study_hours        2     361.1 78621 3128.4
## - test_prep:parent_marital_status         2     404.9 78665 3128.8
## - gender:lunch_type                       1     155.7 78416 3128.9
## - gender:practice_sport                   2     481.8 78742 3129.3
## - is_first_child:wkly_study_hours         2     484.9 78745 3129.4
## <none>                                                78260 3129.7
## - practice_sport:transport_means          2     535.6 78796 3129.8
## - lunch_type:transport_means              1     321.4 78581 3130.1
## - parent_educ:is_first_child              5    1397.5 79657 3130.2
## - lunch_type:wkly_study_hours             2     592.2 78852 3130.2
## - parent_educ:practice_sport             10    2842.9 81103 3130.8
## - ethnic_group:transport_means            4    1371.7 79632 3132.0
## - test_prep:wkly_study_hours              2     944.1 79204 3132.8
## + lunch_type:parent_marital_status        3     368.2 77892 3132.9
## - is_first_child:transport_means          1     745.6 79006 3133.3
## + parent_educ:transport_means             5     837.1 77423 3133.4
## - ethnic_group:is_first_child             4    1603.9 79864 3133.7
## + ethnic_group:test_prep                  4     514.1 77746 3133.8
## + gender:parent_educ                      5     758.5 77501 3134.0
## - parent_marital_status:wkly_study_hours  5    1918.3 80178 3134.0
## + gender:parent_marital_status            3      93.8 78166 3135.0
## + gender:ethnic_group                     4     302.8 77957 3135.4
## + parent_marital_status:practice_sport    5     542.4 77718 3135.6
## - lunch_type:practice_sport               2    1379.3 79639 3136.0
## - parent_marital_status:transport_means   3    1664.3 79924 3136.1
## + parent_educ:test_prep                   5     319.0 77941 3137.3
## + ethnic_group:practice_sport             8    1103.5 77156 3137.3
## + parent_educ:lunch_type                  5     272.2 77988 3137.7
## + ethnic_group:wkly_study_hours           8     800.2 77460 3139.7
## + parent_educ:wkly_study_hours           10    1154.0 77106 3141.0
## - parent_marital_status:is_first_child    2    2180.7 80441 3141.9
## - parent_educ:parent_marital_status      14    5685.1 83945 3143.1
## + ethnic_group:parent_educ               20    2274.4 75986 3152.3
## 
## Step:  AIC=3126.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_marital_status     10    2362.3 80787 3124.5
## - practice_sport:is_first_child           2     234.6 78660 3124.7
## - gender:wkly_study_hours                 2     257.8 78683 3124.9
## - gender:is_first_child                   1       2.9 78428 3125.0
## - gender:transport_means                  1       6.5 78432 3125.0
## - test_prep:transport_means               1      14.0 78439 3125.1
## - lunch_type:is_first_child               1      17.1 78442 3125.1
## - ethnic_group:lunch_type                 4     837.1 79262 3125.2
## - gender:test_prep                        1      37.2 78462 3125.2
## - practice_sport:wkly_study_hours         4     865.2 79290 3125.4
## - lunch_type:test_prep                    1      92.0 78517 3125.7
## - test_prep:is_first_child                1      99.3 78524 3125.7
## - transport_means:wkly_study_hours        2     387.2 78812 3125.9
## - gender:lunch_type                       1     168.8 78594 3126.2
## - test_prep:parent_marital_status         2     444.0 78869 3126.3
## - is_first_child:wkly_study_hours         2     453.2 78878 3126.4
## - practice_sport:transport_means          2     506.4 78931 3126.8
## - gender:practice_sport                   2     509.9 78935 3126.8
## <none>                                                78425 3127.0
## - lunch_type:transport_means              1     319.5 78745 3127.4
## - lunch_type:wkly_study_hours             2     643.8 79069 3127.8
## - parent_educ:practice_sport             10    2891.2 81316 3128.3
## - parent_educ:is_first_child              5    1540.6 79966 3128.4
## - ethnic_group:transport_means            4    1350.2 79775 3129.0
## + test_prep:practice_sport                2     165.1 78260 3129.7
## + lunch_type:parent_marital_status        3     383.1 78042 3130.1
## - test_prep:wkly_study_hours              2     952.3 79377 3130.1
## + parent_educ:transport_means             5     852.2 77573 3130.5
## - is_first_child:transport_means          1     755.8 79181 3130.6
## + gender:parent_educ                      5     805.0 77620 3130.9
## - parent_marital_status:wkly_study_hours  5    1874.3 80299 3130.9
## - ethnic_group:is_first_child             4    1614.4 80040 3131.0
## + ethnic_group:test_prep                  4     497.3 77928 3131.2
## + gender:parent_marital_status            3     119.3 78306 3132.1
## + gender:ethnic_group                     4     285.5 78140 3132.8
## + parent_marital_status:practice_sport    5     529.7 77895 3133.0
## - parent_marital_status:transport_means   3    1654.2 80079 3133.3
## - lunch_type:practice_sport               2    1438.7 79864 3133.7
## + parent_educ:test_prep                   5     295.7 78129 3134.7
## + ethnic_group:practice_sport             8    1085.0 77340 3134.8
## + parent_educ:lunch_type                  5     267.4 78158 3134.9
## + ethnic_group:wkly_study_hours           8     780.9 77644 3137.1
## + parent_educ:wkly_study_hours           10    1191.5 77234 3137.9
## - parent_marital_status:is_first_child    2    2135.4 80561 3138.8
## - parent_educ:parent_marital_status      14    5615.3 84040 3139.8
## + ethnic_group:parent_educ               20    2354.4 76071 3149.0
## 
## Step:  AIC=3124.48
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:is_first_child           2     134.9 80922 3121.5
## - practice_sport:wkly_study_hours         4     706.5 81494 3121.6
## - gender:wkly_study_hours                 2     192.1 80980 3121.9
## - transport_means:wkly_study_hours        2     268.3 81056 3122.4
## - practice_sport:transport_means          2     270.0 81057 3122.4
## - test_prep:parent_marital_status         3     558.2 81346 3122.5
## - test_prep:transport_means               1      12.1 80800 3122.6
## - gender:is_first_child                   1      21.6 80809 3122.6
## - gender:transport_means                  1      26.2 80814 3122.7
## - lunch_type:is_first_child               1      35.8 80823 3122.7
## - ethnic_group:lunch_type                 4     873.8 81661 3122.8
## - parent_educ:practice_sport             10    2583.4 83371 3123.1
## - lunch_type:test_prep                    1      87.2 80875 3123.1
## - gender:test_prep                        1      91.6 80879 3123.2
## - test_prep:is_first_child                1     138.6 80926 3123.5
## - is_first_child:wkly_study_hours         2     434.4 81222 3123.6
## - gender:lunch_type                       1     177.5 80965 3123.8
## - gender:practice_sport                   2     524.9 81312 3124.3
## <none>                                                80787 3124.5
## - lunch_type:wkly_study_hours             2     609.6 81397 3124.9
## - parent_marital_status:wkly_study_hours  6    1735.4 82523 3125.0
## - lunch_type:transport_means              1     384.1 81172 3125.3
## - ethnic_group:is_first_child             4    1283.6 82071 3125.8
## - ethnic_group:transport_means            4    1329.1 82117 3126.1
## - parent_educ:is_first_child              5    1623.5 82411 3126.2
## + ethnic_group:parent_marital_status     10    2362.3 78425 3127.0
## + gender:parent_marital_status            3     436.1 80351 3127.3
## - parent_marital_status:transport_means   3    1233.0 82020 3127.4
## + parent_educ:transport_means             5     917.7 79870 3127.7
## + test_prep:practice_sport                2      91.9 80696 3127.8
## + lunch_type:parent_marital_status        3     338.3 80449 3128.0
## - test_prep:wkly_study_hours              2    1155.0 81942 3128.8
## + ethnic_group:test_prep                  4     446.8 80341 3129.2
## + gender:parent_educ                      5     707.0 80080 3129.3
## - is_first_child:transport_means          1     981.3 81769 3129.6
## + gender:ethnic_group                     4     243.7 80544 3130.7
## + parent_marital_status:practice_sport    6     627.4 80160 3131.9
## - lunch_type:practice_sport               2    1582.8 82370 3131.9
## + parent_educ:test_prep                   5     304.0 80483 3132.2
## + parent_educ:lunch_type                  5     266.7 80521 3132.5
## + ethnic_group:practice_sport             8    1071.0 79716 3132.6
## - parent_marital_status:is_first_child    3    2014.8 82802 3133.0
## - parent_educ:parent_marital_status      15    5583.0 86370 3133.9
## + parent_educ:wkly_study_hours           10    1312.1 79475 3134.8
## + ethnic_group:wkly_study_hours           8     702.7 80085 3135.3
## + ethnic_group:parent_educ               20    2394.3 78393 3146.7
## 
## Step:  AIC=3121.46
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:wkly_study_hours         4     746.1 81668 3118.9
## - gender:wkly_study_hours                 2     197.4 81120 3118.9
## - practice_sport:transport_means          2     256.1 81178 3119.3
## - test_prep:parent_marital_status         3     542.8 81465 3119.4
## - transport_means:wkly_study_hours        2     274.7 81197 3119.5
## - test_prep:transport_means               1      12.3 80935 3119.6
## - gender:is_first_child                   1      25.8 80948 3119.7
## - lunch_type:is_first_child               1      27.4 80950 3119.7
## - gender:transport_means                  1      32.3 80955 3119.7
## - parent_educ:practice_sport             10    2575.3 83498 3119.9
## - ethnic_group:lunch_type                 4     901.1 81823 3120.0
## - lunch_type:test_prep                    1      98.2 81021 3120.2
## - gender:test_prep                        1     100.2 81023 3120.2
## - test_prep:is_first_child                1     105.9 81028 3120.2
## - is_first_child:wkly_study_hours         2     409.4 81332 3120.4
## - gender:lunch_type                       1     186.1 81108 3120.8
## - gender:practice_sport                   2     520.7 81443 3121.2
## <none>                                                80922 3121.5
## - lunch_type:wkly_study_hours             2     614.4 81537 3121.9
## - parent_marital_status:wkly_study_hours  6    1743.9 82666 3122.0
## - lunch_type:transport_means              1     376.8 81299 3122.2
## - ethnic_group:transport_means            4    1280.0 82202 3122.7
## - parent_educ:is_first_child              5    1598.0 82520 3123.0
## - ethnic_group:is_first_child             4    1368.9 82291 3123.4
## - parent_marital_status:transport_means   3    1178.7 82101 3124.0
## + gender:parent_marital_status            3     414.4 80508 3124.4
## + practice_sport:is_first_child           2     134.9 80787 3124.5
## + test_prep:practice_sport                2     104.1 80818 3124.7
## + ethnic_group:parent_marital_status     10    2262.6 78660 3124.7
## + parent_educ:transport_means             5     873.3 80049 3125.1
## + lunch_type:parent_marital_status        3     286.4 80636 3125.4
## - test_prep:wkly_study_hours              2    1121.2 82044 3125.6
## + ethnic_group:test_prep                  4     475.9 80446 3126.0
## + gender:parent_educ                      5     724.6 80198 3126.2
## - is_first_child:transport_means          1    1054.5 81977 3127.1
## + gender:ethnic_group                     4     280.3 80642 3127.4
## - lunch_type:practice_sport               2    1568.5 82491 3128.8
## + parent_educ:test_prep                   5     352.1 80570 3128.9
## + parent_educ:lunch_type                  5     272.5 80650 3129.5
## + parent_marital_status:practice_sport    6     543.3 80379 3129.5
## - parent_marital_status:is_first_child    3    1952.1 82874 3129.5
## + ethnic_group:practice_sport             8    1035.2 79887 3129.9
## - parent_educ:parent_marital_status      15    5525.4 86448 3130.4
## + parent_educ:wkly_study_hours           10    1304.2 79618 3131.9
## + ethnic_group:wkly_study_hours           8     727.5 80195 3132.1
## + ethnic_group:parent_educ               20    2361.2 78561 3144.0
## 
## Step:  AIC=3118.88
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:wkly_study_hours                 2     179.7 81848 3116.2
## - practice_sport:transport_means          2     229.3 81898 3116.5
## - ethnic_group:lunch_type                 4     793.3 82462 3116.6
## - test_prep:parent_marital_status         3     560.0 82228 3116.9
## - test_prep:transport_means               1      11.3 81680 3117.0
## - gender:transport_means                  1      15.7 81684 3117.0
## - transport_means:wkly_study_hours        2     295.9 81964 3117.0
## - parent_educ:practice_sport             10    2564.2 84233 3117.1
## - gender:is_first_child                   1      44.9 81713 3117.2
## - lunch_type:is_first_child               1      69.4 81738 3117.4
## - gender:test_prep                        1      88.2 81757 3117.5
## - lunch_type:test_prep                    1     131.6 81800 3117.8
## - test_prep:is_first_child                1     135.8 81804 3117.9
## - gender:lunch_type                       1     202.3 81871 3118.3
## - is_first_child:wkly_study_hours         2     498.4 82167 3118.5
## <none>                                                81668 3118.9
## - lunch_type:wkly_study_hours             2     556.9 82225 3118.9
## - gender:practice_sport                   2     560.6 82229 3118.9
## - lunch_type:transport_means              1     336.4 82005 3119.3
## - parent_educ:is_first_child              5    1501.0 83169 3119.6
## - parent_marital_status:wkly_study_hours  6    1807.4 83476 3119.8
## - ethnic_group:transport_means            4    1251.4 82920 3119.8
## - ethnic_group:is_first_child             4    1415.5 83084 3121.0
## + practice_sport:wkly_study_hours         4     746.1 80922 3121.5
## + practice_sport:is_first_child           2     174.5 81494 3121.6
## - parent_marital_status:transport_means   3    1236.0 82904 3121.7
## + test_prep:practice_sport                2     136.1 81532 3121.9
## + gender:parent_marital_status            3     401.9 81267 3122.0
## + parent_educ:transport_means             5     945.4 80723 3122.0
## + lunch_type:parent_marital_status        3     219.3 81449 3123.3
## - test_prep:wkly_study_hours              2    1185.6 82854 3123.4
## + ethnic_group:test_prep                  4     471.0 81197 3123.5
## + ethnic_group:parent_marital_status     10    2103.1 79565 3123.5
## + gender:parent_educ                      5     705.1 80963 3123.8
## + gender:ethnic_group                     4     333.0 81335 3124.5
## - is_first_child:transport_means          1    1069.1 82737 3124.6
## - lunch_type:practice_sport               2    1506.1 83174 3125.7
## + parent_educ:test_prep                   5     375.4 81293 3126.2
## + parent_educ:lunch_type                  5     326.2 81342 3126.5
## - parent_educ:parent_marital_status      15    5411.4 87080 3126.7
## - parent_marital_status:is_first_child    3    1942.8 83611 3126.8
## + parent_marital_status:practice_sport    6     469.0 81199 3127.5
## + ethnic_group:practice_sport             8     969.6 80699 3127.8
## + ethnic_group:wkly_study_hours           8     807.6 80861 3129.0
## + parent_educ:wkly_study_hours           10    1140.4 80528 3130.6
## + ethnic_group:parent_educ               20    2482.9 79186 3140.7
## 
## Step:  AIC=3116.17
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:lunch_type + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:lunch_type                 4     791.6 82640 3113.8
## - practice_sport:transport_means          2     245.4 82094 3113.9
## - test_prep:parent_marital_status         3     545.1 82393 3114.1
## - test_prep:transport_means               1      11.0 81859 3114.2
## - transport_means:wkly_study_hours        2     290.0 82138 3114.3
## - gender:transport_means                  1      18.5 81867 3114.3
## - parent_educ:practice_sport             10    2558.1 84406 3114.3
## - gender:is_first_child                   1      48.8 81897 3114.5
## - lunch_type:is_first_child               1      68.8 81917 3114.7
## - gender:test_prep                        1     110.7 81959 3115.0
## - lunch_type:test_prep                    1     122.5 81971 3115.1
## - test_prep:is_first_child                1     162.3 82010 3115.3
## - gender:lunch_type                       1     171.5 82020 3115.4
## - is_first_child:wkly_study_hours         2     495.3 82343 3115.7
## - lunch_type:wkly_study_hours             2     509.0 82357 3115.8
## <none>                                                81848 3116.2
## - gender:practice_sport                   2     570.2 82418 3116.3
## - lunch_type:transport_means              1     328.3 82176 3116.5
## - parent_educ:is_first_child              5    1504.7 83353 3116.9
## - ethnic_group:transport_means            4    1252.8 83101 3117.1
## - ethnic_group:is_first_child             4    1338.1 83186 3117.7
## - parent_marital_status:wkly_study_hours  6    2060.0 83908 3118.8
## + practice_sport:is_first_child           2     182.7 81665 3118.9
## + gender:wkly_study_hours                 2     179.7 81668 3118.9
## - parent_marital_status:transport_means   3    1218.2 83066 3118.9
## + practice_sport:wkly_study_hours         4     728.4 81120 3118.9
## + test_prep:practice_sport                2     138.9 81709 3119.2
## + gender:parent_marital_status            3     407.2 81441 3119.2
## + parent_educ:transport_means             5     888.5 80960 3119.7
## - test_prep:wkly_study_hours              2    1175.5 83024 3120.6
## + lunch_type:parent_marital_status        3     191.5 81657 3120.8
## + gender:parent_educ                      5     730.7 81117 3120.9
## + ethnic_group:test_prep                  4     436.0 81412 3121.0
## + ethnic_group:parent_marital_status     10    2063.5 79785 3121.1
## - is_first_child:transport_means          1    1003.7 82852 3121.4
## + gender:ethnic_group                     4     373.8 81474 3121.5
## - lunch_type:practice_sport               2    1498.1 83346 3122.9
## - parent_marital_status:is_first_child    3    1869.2 83717 3123.5
## + parent_educ:test_prep                   5     367.9 81480 3123.5
## - parent_educ:parent_marital_status      15    5370.9 87219 3123.7
## + parent_educ:lunch_type                  5     307.2 81541 3124.0
## + parent_marital_status:practice_sport    6     474.3 81374 3124.8
## + ethnic_group:practice_sport             8    1015.8 80832 3124.8
## + ethnic_group:wkly_study_hours           8     786.1 81062 3126.5
## + parent_educ:wkly_study_hours           10    1222.9 80625 3127.3
## + ethnic_group:parent_educ               20    2486.4 79362 3138.0
## 
## Step:  AIC=3113.85
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:transport_means          2     207.3 82847 3111.3
## - parent_educ:practice_sport             10    2516.6 85156 3111.6
## - test_prep:transport_means               1      10.1 82650 3111.9
## - gender:transport_means                  1      13.8 82653 3111.9
## - gender:is_first_child                   1      41.3 82681 3112.2
## - transport_means:wkly_study_hours        2     339.2 82979 3112.3
## - test_prep:parent_marital_status         3     629.1 83269 3112.3
## - lunch_type:is_first_child               1      80.4 82720 3112.4
## - gender:test_prep                        1     135.3 82775 3112.8
## - test_prep:is_first_child                1     142.8 82782 3112.9
## - lunch_type:test_prep                    1     144.5 82784 3112.9
## - lunch_type:wkly_study_hours             2     428.9 83069 3112.9
## - gender:lunch_type                       1     191.2 82831 3113.2
## - gender:practice_sport                   2     488.0 83128 3113.3
## - is_first_child:wkly_study_hours         2     498.0 83138 3113.4
## <none>                                                82640 3113.8
## - ethnic_group:is_first_child             4    1132.4 83772 3113.9
## - ethnic_group:transport_means            4    1167.1 83807 3114.1
## - parent_educ:is_first_child              5    1534.0 84174 3114.7
## - lunch_type:transport_means              1     438.1 83078 3115.0
## - parent_marital_status:transport_means   3    1154.2 83794 3116.0
## + ethnic_group:lunch_type                 4     791.6 81848 3116.2
## + practice_sport:is_first_child           2     203.4 82436 3116.4
## + test_prep:practice_sport                2     188.0 82452 3116.5
## + gender:wkly_study_hours                 2     178.0 82462 3116.6
## - parent_marital_status:wkly_study_hours  6    2096.2 84736 3116.6
## + parent_educ:transport_means             5     990.3 81649 3116.7
## + gender:parent_marital_status            3     400.6 82239 3117.0
## + practice_sport:wkly_study_hours         4     624.4 82015 3117.4
## + ethnic_group:parent_marital_status     10    2132.2 80507 3118.4
## + lunch_type:parent_marital_status        3     186.2 82454 3118.5
## - test_prep:wkly_study_hours              2    1230.2 83870 3118.6
## - is_first_child:transport_means          1     991.0 83631 3118.9
## + ethnic_group:test_prep                  4     387.6 82252 3119.1
## + gender:ethnic_group                     4     380.7 82259 3119.1
## + gender:parent_educ                      5     625.8 82014 3119.4
## - parent_educ:parent_marital_status      15    5161.0 87801 3119.6
## - parent_marital_status:is_first_child    3    1814.6 84454 3120.7
## + parent_educ:test_prep                   5     407.8 82232 3120.9
## - lunch_type:practice_sport               2    1597.2 84237 3121.2
## + parent_educ:lunch_type                  5     333.4 82306 3121.5
## + ethnic_group:practice_sport             8    1057.8 81582 3122.2
## + parent_marital_status:practice_sport    6     482.2 82158 3122.4
## + ethnic_group:wkly_study_hours           8     816.7 81823 3124.0
## + parent_educ:wkly_study_hours           10    1061.0 81579 3126.2
## + ethnic_group:parent_educ               20    2629.1 80011 3134.8
## 
## Step:  AIC=3111.33
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:practice_sport             10    2466.4 85313 3108.6
## - test_prep:transport_means               1       7.1 82854 3109.4
## - gender:transport_means                  1      13.8 82861 3109.4
## - gender:is_first_child                   1      56.2 82903 3109.7
## - lunch_type:is_first_child               1      71.3 82918 3109.8
## - transport_means:wkly_study_hours        2     357.8 83205 3109.9
## - test_prep:parent_marital_status         3     644.8 83492 3109.9
## - gender:test_prep                        1     131.9 82979 3110.3
## - lunch_type:wkly_study_hours             2     420.4 83267 3110.3
## - test_prep:is_first_child                1     147.4 82994 3110.4
## - lunch_type:test_prep                    1     170.0 83017 3110.5
## - gender:practice_sport                   2     458.5 83305 3110.6
## - gender:lunch_type                       1     191.5 83039 3110.7
## - is_first_child:wkly_study_hours         2     491.5 83338 3110.8
## - ethnic_group:is_first_child             4    1114.2 83961 3111.2
## <none>                                                82847 3111.3
## - ethnic_group:transport_means            4    1218.0 84065 3111.9
## - parent_educ:is_first_child              5    1544.3 84391 3112.2
## - lunch_type:transport_means              1     450.3 83297 3112.5
## - parent_marital_status:transport_means   3    1149.8 83997 3113.5
## + practice_sport:transport_means          2     207.3 82640 3113.8
## + ethnic_group:lunch_type                 4     753.5 82094 3113.9
## + gender:wkly_study_hours                 2     193.1 82654 3113.9
## + practice_sport:is_first_child           2     183.8 82663 3114.0
## + test_prep:practice_sport                2     173.2 82674 3114.1
## - parent_marital_status:wkly_study_hours  6    2116.7 84964 3114.2
## + gender:parent_marital_status            3     364.2 82483 3114.7
## + practice_sport:wkly_study_hours         4     605.0 82242 3115.0
## + parent_educ:transport_means             5     874.3 81973 3115.1
## + lunch_type:parent_marital_status        3     180.4 82667 3116.0
## - test_prep:wkly_study_hours              2    1235.2 84082 3116.1
## + ethnic_group:test_prep                  4     396.0 82451 3116.5
## + gender:ethnic_group                     4     377.0 82470 3116.6
## - parent_educ:parent_marital_status      15    5138.6 87986 3116.8
## - is_first_child:transport_means          1    1062.2 83909 3116.8
## + gender:parent_educ                      5     597.8 82249 3117.1
## + ethnic_group:parent_marital_status     10    1954.3 80893 3117.2
## - parent_marital_status:is_first_child    3    1809.3 84656 3118.1
## + parent_educ:test_prep                   5     434.0 82413 3118.2
## - lunch_type:practice_sport               2    1585.6 84433 3118.5
## + parent_educ:lunch_type                  5     376.4 82471 3118.6
## + ethnic_group:practice_sport             8    1073.6 81773 3119.6
## + parent_marital_status:practice_sport    6     447.4 82400 3120.1
## + ethnic_group:wkly_study_hours           8     821.6 82025 3121.4
## + parent_educ:wkly_study_hours           10    1023.1 81824 3124.0
## + ethnic_group:parent_educ               20    2651.9 80195 3132.1
## 
## Step:  AIC=3108.64
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:parent_marital_status         3     528.2 85842 3106.3
## - transport_means:wkly_study_hours        2     252.8 85566 3106.4
## - test_prep:transport_means               1       6.1 85320 3106.7
## - gender:transport_means                  1      53.5 85367 3107.0
## - gender:is_first_child                   1      69.0 85382 3107.1
## - gender:practice_sport                   2     371.9 85685 3107.2
## - lunch_type:is_first_child               1      89.0 85402 3107.2
## - gender:lunch_type                       1     128.6 85442 3107.5
## - lunch_type:test_prep                    1     168.7 85482 3107.8
## - gender:test_prep                        1     169.6 85483 3107.8
## - test_prep:is_first_child                1     189.4 85503 3107.9
## - is_first_child:wkly_study_hours         2     501.2 85815 3108.1
## - lunch_type:wkly_study_hours             2     501.8 85815 3108.1
## <none>                                                85313 3108.6
## - ethnic_group:is_first_child             4    1176.4 86490 3108.7
## - lunch_type:transport_means              1     350.4 85664 3109.1
## - ethnic_group:transport_means            4    1384.3 86698 3110.1
## - test_prep:wkly_study_hours              2     930.9 86244 3111.0
## + parent_educ:practice_sport             10    2466.4 82847 3111.3
## + gender:wkly_study_hours                 2     187.2 85126 3111.3
## - parent_educ:is_first_child              5    1861.6 87175 3111.4
## + practice_sport:is_first_child           2     173.2 85140 3111.4
## + test_prep:practice_sport                2     172.7 85141 3111.4
## + practice_sport:transport_means          2     157.1 85156 3111.6
## + ethnic_group:lunch_type                 4     725.6 84588 3111.6
## - parent_marital_status:wkly_study_hours  6    2229.8 87543 3111.9
## - parent_marital_status:transport_means   3    1345.0 86658 3111.9
## + gender:parent_marital_status            3     380.5 84933 3112.0
## - is_first_child:transport_means          1     813.3 86127 3112.2
## + practice_sport:wkly_study_hours         4     575.3 84738 3112.7
## + parent_educ:transport_means             5     848.1 84465 3112.7
## - lunch_type:practice_sport               2    1258.9 86572 3113.3
## + lunch_type:parent_marital_status        3     167.1 85146 3113.5
## + ethnic_group:test_prep                  4     430.7 84883 3113.7
## + gender:ethnic_group                     4     394.4 84919 3113.9
## + gender:parent_educ                      5     656.9 84657 3114.1
## - parent_marital_status:is_first_child    3    1770.1 87084 3114.8
## + parent_educ:lunch_type                  5     556.2 84757 3114.8
## + parent_educ:test_prep                   5     401.2 84912 3115.9
## + ethnic_group:practice_sport             8    1164.5 84149 3116.5
## - parent_educ:parent_marital_status      15    5674.3 90988 3116.6
## + ethnic_group:parent_marital_status     10    1651.0 83662 3117.1
## + parent_marital_status:practice_sport    6     334.6 84979 3118.3
## + ethnic_group:wkly_study_hours           8     773.4 84540 3119.3
## + parent_educ:wkly_study_hours           10    1137.2 84176 3120.7
## + ethnic_group:parent_educ               20    2585.1 82728 3130.5
## 
## Step:  AIC=3106.28
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - transport_means:wkly_study_hours        2     246.8 86088 3104.0
## - test_prep:transport_means               1      16.2 85858 3104.4
## - gender:transport_means                  1      41.8 85883 3104.6
## - lunch_type:is_first_child               1      80.3 85922 3104.8
## - gender:is_first_child                   1      80.8 85922 3104.8
## - gender:practice_sport                   2     391.2 86233 3105.0
## - gender:lunch_type                       1     133.0 85975 3105.2
## - gender:test_prep                        1     156.6 85998 3105.4
## - lunch_type:test_prep                    1     167.4 86009 3105.4
## - lunch_type:wkly_study_hours             2     517.9 86359 3105.8
## - is_first_child:wkly_study_hours         2     539.2 86381 3106.0
## - test_prep:is_first_child                1     264.1 86106 3106.1
## <none>                                                85842 3106.3
## - ethnic_group:is_first_child             4    1209.8 87051 3106.5
## - lunch_type:transport_means              1     355.0 86197 3106.7
## - ethnic_group:transport_means            4    1370.0 87212 3107.6
## - parent_educ:is_first_child              5    1803.5 87645 3108.6
## - test_prep:wkly_study_hours              2     922.7 86764 3108.6
## + test_prep:parent_marital_status         3     528.2 85313 3108.6
## + test_prep:practice_sport                2     227.2 85614 3108.7
## + ethnic_group:lunch_type                 4     794.7 85047 3108.8
## + gender:wkly_study_hours                 2     191.1 85650 3109.0
## + practice_sport:transport_means          2     166.2 85675 3109.1
## + practice_sport:is_first_child           2     165.9 85676 3109.1
## - parent_marital_status:wkly_study_hours  6    2221.9 88063 3109.4
## - is_first_child:transport_means          1     764.1 86606 3109.5
## + parent_educ:practice_sport             10    2349.8 83492 3109.9
## - parent_marital_status:transport_means   3    1470.4 87312 3110.3
## + gender:parent_marital_status            3     286.9 85555 3110.3
## + parent_educ:transport_means             5     862.9 84979 3110.3
## + practice_sport:wkly_study_hours         4     547.4 85294 3110.5
## - lunch_type:practice_sport               2    1236.0 87078 3110.7
## + lunch_type:parent_marital_status        3     214.5 85627 3110.8
## + gender:ethnic_group                     4     426.1 85415 3111.3
## + ethnic_group:test_prep                  4     419.6 85422 3111.4
## + gender:parent_educ                      5     621.8 85220 3112.0
## + parent_educ:lunch_type                  5     563.6 85278 3112.4
## - parent_educ:parent_marital_status      15    5469.5 91311 3112.7
## - parent_marital_status:is_first_child    3    1845.3 87687 3112.8
## + parent_educ:test_prep                   5     377.3 85464 3113.7
## + ethnic_group:practice_sport             8    1128.8 84713 3114.5
## + parent_marital_status:practice_sport    6     382.9 85459 3115.6
## + ethnic_group:parent_marital_status     11    1760.9 84081 3116.1
## + ethnic_group:wkly_study_hours           8     867.5 84974 3116.3
## + parent_educ:wkly_study_hours           10    1216.0 84626 3117.9
## + ethnic_group:parent_educ               20    2671.7 83170 3127.6
## 
## Step:  AIC=3103.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:transport_means               1       7.5 86096 3102.0
## - gender:transport_means                  1      39.1 86127 3102.2
## - gender:is_first_child                   1      67.5 86156 3102.4
## - lunch_type:is_first_child               1      74.0 86162 3102.5
## - gender:lunch_type                       1     121.2 86210 3102.8
## - gender:practice_sport                   2     425.9 86514 3102.9
## - gender:test_prep                        1     140.2 86228 3102.9
## - lunch_type:test_prep                    1     153.5 86242 3103.0
## - lunch_type:wkly_study_hours             2     549.2 86638 3103.7
## - test_prep:is_first_child                1     279.5 86368 3103.9
## <none>                                                86088 3104.0
## - is_first_child:wkly_study_hours         2     592.9 86681 3104.0
## - lunch_type:transport_means              1     345.6 86434 3104.3
## - ethnic_group:is_first_child             4    1229.5 87318 3104.3
## - test_prep:wkly_study_hours              2     872.0 86960 3105.9
## - ethnic_group:transport_means            4    1465.2 87554 3105.9
## + test_prep:practice_sport                2     258.1 85830 3106.2
## + ethnic_group:lunch_type                 4     835.7 85253 3106.2
## + transport_means:wkly_study_hours        2     246.8 85842 3106.3
## + test_prep:parent_marital_status         3     522.1 85566 3106.4
## - parent_educ:is_first_child              5    1848.6 87937 3106.5
## + practice_sport:transport_means          2     184.0 85904 3106.7
## + practice_sport:is_first_child           2     182.1 85906 3106.7
## + gender:wkly_study_hours                 2     180.1 85908 3106.7
## - is_first_child:transport_means          1     769.9 86858 3107.2
## - parent_marital_status:wkly_study_hours  6    2303.2 88392 3107.6
## - parent_marital_status:transport_means   3    1454.0 87542 3107.9
## + practice_sport:wkly_study_hours         4     564.7 85524 3108.1
## + gender:parent_marital_status            3     272.1 85816 3108.1
## + parent_educ:practice_sport             10    2249.6 83839 3108.3
## + parent_educ:transport_means             5     808.8 85280 3108.4
## + lunch_type:parent_marital_status        3     219.1 85869 3108.5
## - lunch_type:practice_sport               2    1254.1 87342 3108.5
## + gender:ethnic_group                     4     458.6 85630 3108.8
## + ethnic_group:test_prep                  4     414.0 85674 3109.1
## + gender:parent_educ                      5     674.2 85414 3109.3
## + parent_educ:lunch_type                  5     590.9 85497 3109.9
## - parent_marital_status:is_first_child    3    1791.3 87880 3110.1
## - parent_educ:parent_marital_status      15    5445.9 91534 3110.2
## + parent_educ:test_prep                   5     377.4 85711 3111.4
## + ethnic_group:practice_sport             8    1152.6 84936 3112.0
## + parent_marital_status:practice_sport    6     396.9 85691 3113.2
## + ethnic_group:parent_marital_status     11    1695.5 84393 3114.2
## + ethnic_group:wkly_study_hours           8     714.6 85374 3115.1
## + parent_educ:wkly_study_hours           10    1220.0 84868 3115.6
## + ethnic_group:parent_educ               20    2613.0 83475 3125.8
## 
## Step:  AIC=3102.03
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:transport_means                  1      42.1 86138 3100.3
## - gender:is_first_child                   1      67.9 86164 3100.5
## - lunch_type:is_first_child               1      77.5 86173 3100.6
## - gender:lunch_type                       1     124.5 86220 3100.9
## - gender:practice_sport                   2     423.6 86519 3100.9
## - gender:test_prep                        1     138.2 86234 3101.0
## - lunch_type:test_prep                    1     154.4 86250 3101.1
## - lunch_type:wkly_study_hours             2     541.9 86638 3101.7
## - test_prep:is_first_child                1     280.9 86377 3101.9
## <none>                                                86096 3102.0
## - is_first_child:wkly_study_hours         2     601.9 86698 3102.1
## - ethnic_group:is_first_child             4    1222.9 87319 3102.3
## - lunch_type:transport_means              1     341.8 86438 3102.4
## - test_prep:wkly_study_hours              2     866.7 86963 3103.9
## + test_prep:transport_means               1       7.5 86088 3104.0
## - ethnic_group:transport_means            4    1483.7 87580 3104.1
## + test_prep:practice_sport                2     258.8 85837 3104.2
## + ethnic_group:lunch_type                 4     837.4 85258 3104.3
## + transport_means:wkly_study_hours        2     238.0 85858 3104.4
## + test_prep:parent_marital_status         3     528.2 85568 3104.4
## - parent_educ:is_first_child              5    1853.3 87949 3104.6
## + practice_sport:is_first_child           2     182.2 85914 3104.8
## + gender:wkly_study_hours                 2     181.4 85914 3104.8
## + practice_sport:transport_means          2     180.8 85915 3104.8
## - is_first_child:transport_means          1     780.2 86876 3105.3
## - parent_marital_status:wkly_study_hours  6    2299.8 88396 3105.6
## - parent_marital_status:transport_means   3    1462.4 87558 3106.0
## + practice_sport:wkly_study_hours         4     564.1 85532 3106.2
## + gender:parent_marital_status            3     270.0 85826 3106.2
## + parent_educ:practice_sport             10    2248.9 83847 3106.4
## + parent_educ:transport_means             5     812.6 85283 3106.4
## + lunch_type:parent_marital_status        3     221.2 85875 3106.5
## - lunch_type:practice_sport               2    1259.1 87355 3106.6
## + gender:ethnic_group                     4     457.3 85638 3106.9
## + ethnic_group:test_prep                  4     413.8 85682 3107.2
## + gender:parent_educ                      5     671.4 85424 3107.4
## + parent_educ:lunch_type                  5     584.8 85511 3108.0
## - parent_marital_status:is_first_child    3    1800.2 87896 3108.2
## - parent_educ:parent_marital_status      15    5477.3 91573 3108.4
## + parent_educ:test_prep                   5     381.9 85714 3109.4
## + ethnic_group:practice_sport             8    1155.8 84940 3110.1
## + parent_marital_status:practice_sport    6     398.4 85697 3111.3
## + ethnic_group:parent_marital_status     11    1694.7 84401 3112.3
## + ethnic_group:wkly_study_hours           8     716.5 85379 3113.1
## + parent_educ:wkly_study_hours           10    1221.4 84874 3113.6
## + ethnic_group:parent_educ               20    2587.1 83509 3124.0
## 
## Step:  AIC=3100.31
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:is_first_child                   1      67.1 86205 3098.8
## - lunch_type:is_first_child               1      87.1 86225 3098.9
## - gender:test_prep                        1     125.8 86264 3099.2
## - gender:lunch_type                       1     127.9 86266 3099.2
## - gender:practice_sport                   2     441.0 86579 3099.3
## - lunch_type:test_prep                    1     157.7 86296 3099.4
## - lunch_type:wkly_study_hours             2     527.4 86665 3099.9
## - test_prep:is_first_child                1     287.0 86425 3100.3
## <none>                                                86138 3100.3
## - is_first_child:wkly_study_hours         2     614.1 86752 3100.5
## - ethnic_group:is_first_child             4    1217.0 87355 3100.6
## - lunch_type:transport_means              1     350.7 86489 3100.7
## + gender:transport_means                  1      42.1 86096 3102.0
## - test_prep:wkly_study_hours              2     865.7 87004 3102.2
## + test_prep:transport_means               1      10.5 86127 3102.2
## - ethnic_group:transport_means            4    1467.2 87605 3102.3
## + test_prep:practice_sport                2     254.5 85883 3102.6
## + ethnic_group:lunch_type                 4     830.4 85308 3102.6
## + transport_means:wkly_study_hours        2     233.9 85904 3102.7
## + test_prep:parent_marital_status         3     517.8 85620 3102.8
## - parent_educ:is_first_child              5    1840.1 87978 3102.8
## + gender:wkly_study_hours                 2     185.9 85952 3103.0
## + practice_sport:is_first_child           2     184.7 85953 3103.1
## + practice_sport:transport_means          2     182.4 85956 3103.1
## - is_first_child:transport_means          1     803.3 86941 3103.8
## - parent_marital_status:wkly_study_hours  6    2297.0 88435 3103.8
## - parent_marital_status:transport_means   3    1462.1 87600 3104.2
## + parent_educ:practice_sport             10    2282.9 83855 3104.5
## + gender:parent_marital_status            3     264.9 85873 3104.5
## + practice_sport:wkly_study_hours         4     542.5 85595 3104.6
## + parent_educ:transport_means             5     823.1 85315 3104.7
## - lunch_type:practice_sport               2    1240.0 87378 3104.8
## + lunch_type:parent_marital_status        3     222.7 85915 3104.8
## + gender:ethnic_group                     4     473.5 85664 3105.1
## + ethnic_group:test_prep                  4     412.7 85725 3105.5
## + gender:parent_educ                      5     671.3 85467 3105.7
## + parent_educ:lunch_type                  5     591.3 85547 3106.2
## - parent_educ:parent_marital_status      15    5443.9 91582 3106.5
## - parent_marital_status:is_first_child    3    1820.2 87958 3106.7
## + parent_educ:test_prep                   5     385.7 85752 3107.7
## + ethnic_group:practice_sport             8    1140.5 84997 3108.4
## + parent_marital_status:practice_sport    6     390.6 85747 3109.6
## + ethnic_group:parent_marital_status     11    1717.1 84421 3110.4
## + ethnic_group:wkly_study_hours           8     709.6 85428 3111.4
## + parent_educ:wkly_study_hours           10    1196.9 84941 3112.1
## + ethnic_group:parent_educ               20    2560.8 83577 3122.5
## 
## Step:  AIC=3098.77
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:is_first_child + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:is_first_child               1      97.8 86303 3097.4
## - gender:test_prep                        1     115.8 86321 3097.6
## - gender:lunch_type                       1     127.1 86332 3097.6
## - gender:practice_sport                   2     456.8 86662 3097.9
## - lunch_type:test_prep                    1     169.6 86375 3097.9
## - lunch_type:wkly_study_hours             2     528.1 86733 3098.4
## <none>                                                86205 3098.8
## - ethnic_group:is_first_child             4    1184.1 87389 3098.8
## - test_prep:is_first_child                1     315.6 86521 3098.9
## - is_first_child:wkly_study_hours         2     648.1 86853 3099.2
## - lunch_type:transport_means              1     367.7 86573 3099.3
## + gender:is_first_child                   1      67.1 86138 3100.3
## + gender:transport_means                  1      41.3 86164 3100.5
## - test_prep:wkly_study_hours              2     849.9 87055 3100.6
## + test_prep:transport_means               1      10.9 86194 3100.7
## - ethnic_group:transport_means            4    1518.3 87723 3101.1
## + test_prep:practice_sport                2     241.4 85964 3101.1
## + ethnic_group:lunch_type                 4     819.4 85386 3101.1
## + test_prep:parent_marital_status         3     527.3 85678 3101.2
## + transport_means:wkly_study_hours        2     221.2 85984 3101.3
## + practice_sport:transport_means          2     193.8 86011 3101.4
## + practice_sport:is_first_child           2     192.0 86013 3101.5
## + gender:wkly_study_hours                 2     185.4 86020 3101.5
## - parent_educ:is_first_child              5    1889.5 88095 3101.6
## - parent_marital_status:wkly_study_hours  6    2259.4 88464 3102.0
## - is_first_child:transport_means          1     777.0 86982 3102.1
## + gender:parent_marital_status            3     287.2 85918 3102.8
## + parent_educ:practice_sport             10    2295.0 83910 3102.8
## + practice_sport:wkly_study_hours         4     562.1 85643 3102.9
## - parent_marital_status:transport_means   3    1506.1 87711 3103.0
## + parent_educ:transport_means             5     813.9 85391 3103.2
## + lunch_type:parent_marital_status        3     232.4 85973 3103.2
## + gender:ethnic_group                     4     489.0 85716 3103.4
## - lunch_type:practice_sport               2    1289.5 87495 3103.5
## + ethnic_group:test_prep                  4     394.8 85810 3104.1
## + gender:parent_educ                      5     664.8 85540 3104.2
## + parent_educ:lunch_type                  5     631.3 85574 3104.4
## - parent_educ:parent_marital_status      15    5457.7 91663 3105.0
## - parent_marital_status:is_first_child    3    1805.4 88011 3105.0
## + parent_educ:test_prep                   5     387.6 85818 3106.1
## + ethnic_group:practice_sport             8    1096.1 85109 3107.2
## + parent_marital_status:practice_sport    6     389.2 85816 3108.1
## + ethnic_group:parent_marital_status     11    1738.0 84467 3108.8
## + ethnic_group:wkly_study_hours           8     685.9 85519 3110.1
## + parent_educ:wkly_study_hours           10    1203.7 85001 3110.5
## + ethnic_group:parent_educ               20    2490.6 83714 3121.5
## 
## Step:  AIC=3097.44
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:lunch_type                       1     120.4 86423 3096.3
## - gender:test_prep                        1     122.5 86425 3096.3
## - gender:practice_sport                   2     425.3 86728 3096.3
## - lunch_type:test_prep                    1     164.4 86467 3096.6
## - lunch_type:wkly_study_hours             2     507.0 86810 3096.9
## - ethnic_group:is_first_child             4    1131.4 87434 3097.1
## <none>                                                86303 3097.4
## - test_prep:is_first_child                1     293.8 86597 3097.4
## - is_first_child:wkly_study_hours         2     610.4 86913 3097.6
## - lunch_type:transport_means              1     380.8 86684 3098.0
## + lunch_type:is_first_child               1      97.8 86205 3098.8
## + gender:is_first_child                   1      77.8 86225 3098.9
## + gender:transport_means                  1      51.4 86251 3099.1
## - test_prep:wkly_study_hours              2     862.1 87165 3099.3
## + test_prep:transport_means               1      16.2 86287 3099.3
## + ethnic_group:lunch_type                 4     823.2 85480 3099.8
## + test_prep:practice_sport                2     235.1 86068 3099.8
## + test_prep:parent_marital_status         3     520.4 85782 3099.9
## - ethnic_group:transport_means            4    1548.9 87852 3099.9
## + transport_means:wkly_study_hours        2     211.8 86091 3100.0
## + gender:wkly_study_hours                 2     188.5 86114 3100.2
## + practice_sport:transport_means          2     184.2 86119 3100.2
## - parent_educ:is_first_child              5    1885.0 88188 3100.2
## + practice_sport:is_first_child           2     175.0 86128 3100.2
## - parent_marital_status:wkly_study_hours  6    2200.8 88504 3100.3
## - is_first_child:transport_means          1     770.4 87073 3100.7
## + practice_sport:wkly_study_hours         4     603.6 85699 3101.3
## + parent_educ:practice_sport             10    2322.3 83981 3101.3
## + gender:parent_marital_status            3     297.0 86006 3101.4
## - parent_marital_status:transport_means   3    1515.9 87819 3101.7
## + parent_educ:transport_means             5     822.3 85481 3101.8
## + lunch_type:parent_marital_status        3     227.7 86075 3101.9
## - lunch_type:practice_sport               2    1285.2 87588 3102.2
## + gender:ethnic_group                     4     468.8 85834 3102.2
## + ethnic_group:test_prep                  4     412.9 85890 3102.6
## + gender:parent_educ                      5     671.5 85631 3102.8
## + parent_educ:lunch_type                  5     648.6 85654 3103.0
## - parent_marital_status:is_first_child    3    1733.5 88036 3103.2
## - parent_educ:parent_marital_status      15    5422.1 91725 3103.4
## + parent_educ:test_prep                   5     411.8 85891 3104.6
## + ethnic_group:practice_sport             8    1075.2 85228 3106.1
## + parent_marital_status:practice_sport    6     390.2 85913 3106.8
## + ethnic_group:parent_marital_status     11    1745.0 84558 3107.4
## + ethnic_group:wkly_study_hours           8     686.4 85616 3108.7
## + parent_educ:wkly_study_hours           10    1226.0 85077 3109.0
## + ethnic_group:parent_educ               20    2445.0 83858 3120.5
## 
## Step:  AIC=3096.27
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:is_first_child + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:test_prep                        1     108.1 86531 3095.0
## - gender:practice_sport                   2     419.0 86842 3095.1
## - lunch_type:test_prep                    1     190.0 86613 3095.6
## - lunch_type:wkly_study_hours             2     492.0 86915 3095.6
## - ethnic_group:is_first_child             4    1110.9 87534 3095.8
## <none>                                                86423 3096.3
## - test_prep:is_first_child                1     303.9 86727 3096.3
## - is_first_child:wkly_study_hours         2     606.7 87030 3096.4
## - lunch_type:transport_means              1     408.7 86832 3097.1
## + gender:lunch_type                       1     120.4 86303 3097.4
## + lunch_type:is_first_child               1      91.2 86332 3097.6
## + gender:is_first_child                   1      76.5 86347 3097.7
## + gender:transport_means                  1      54.6 86369 3097.9
## + test_prep:transport_means               1      20.8 86403 3098.1
## - test_prep:wkly_study_hours              2     879.1 87302 3098.2
## + test_prep:practice_sport                2     250.2 86173 3098.6
## + ethnic_group:lunch_type                 4     828.1 85595 3098.6
## + test_prep:parent_marital_status         3     526.2 85897 3098.7
## + transport_means:wkly_study_hours        2     200.0 86223 3098.9
## - ethnic_group:transport_means            4    1576.0 87999 3098.9
## + practice_sport:transport_means          2     181.2 86242 3099.0
## + gender:wkly_study_hours                 2     166.1 86257 3099.1
## + practice_sport:is_first_child           2     161.1 86262 3099.2
## - parent_educ:is_first_child              5    1917.3 88341 3099.2
## - is_first_child:transport_means          1     743.5 87167 3099.3
## - parent_marital_status:wkly_study_hours  6    2284.1 88707 3099.7
## + practice_sport:wkly_study_hours         4     602.7 85821 3100.1
## - parent_marital_status:transport_means   3    1475.8 87899 3100.3
## + gender:parent_marital_status            3     286.4 86137 3100.3
## + parent_educ:transport_means             5     855.6 85568 3100.4
## + parent_educ:practice_sport             10    2280.1 84143 3100.5
## + lunch_type:parent_marital_status        3     258.2 86165 3100.5
## + gender:ethnic_group                     4     457.4 85966 3101.1
## + ethnic_group:test_prep                  4     418.7 86005 3101.4
## + parent_educ:lunch_type                  5     696.7 85727 3101.5
## - lunch_type:practice_sport               2    1371.9 87795 3101.6
## - parent_marital_status:is_first_child    3    1685.0 88108 3101.7
## + gender:parent_educ                      5     664.3 85759 3101.7
## - parent_educ:parent_marital_status      15    5394.8 91818 3102.0
## + parent_educ:test_prep                   5     394.9 86028 3103.6
## + ethnic_group:practice_sport             8    1026.1 85397 3105.2
## + parent_marital_status:practice_sport    6     401.4 86022 3105.5
## + ethnic_group:parent_marital_status     11    1748.2 84675 3106.2
## + ethnic_group:wkly_study_hours           8     702.1 85721 3107.4
## + parent_educ:wkly_study_hours           10    1177.1 85246 3108.2
## + ethnic_group:parent_educ               20    2371.1 84052 3119.8
## 
## Step:  AIC=3095
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:is_first_child + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:practice_sport                   2     441.2 86973 3094.0
## - ethnic_group:is_first_child             4    1074.7 87606 3094.3
## - lunch_type:test_prep                    1     207.3 86739 3094.4
## - lunch_type:wkly_study_hours             2     504.2 87036 3094.4
## <none>                                                86531 3095.0
## - test_prep:is_first_child                1     303.6 86835 3095.1
## - is_first_child:wkly_study_hours         2     612.5 87144 3095.2
## - lunch_type:transport_means              1     426.8 86958 3095.9
## + gender:test_prep                        1     108.1 86423 3096.3
## + gender:lunch_type                       1     106.0 86425 3096.3
## + lunch_type:is_first_child               1      97.7 86434 3096.3
## + gender:is_first_child                   1      66.6 86465 3096.6
## + gender:transport_means                  1      41.4 86490 3096.7
## - test_prep:wkly_study_hours              2     845.9 87377 3096.7
## + test_prep:transport_means               1      17.0 86514 3096.9
## + ethnic_group:lunch_type                 4     846.4 85685 3097.2
## + test_prep:practice_sport                2     243.1 86288 3097.3
## + test_prep:parent_marital_status         3     516.8 86015 3097.5
## - parent_educ:is_first_child              5    1876.5 88408 3097.7
## + gender:wkly_study_hours                 2     188.8 86343 3097.7
## + transport_means:wkly_study_hours        2     188.1 86343 3097.7
## - ethnic_group:transport_means            4    1587.4 88119 3097.7
## + practice_sport:transport_means          2     173.6 86358 3097.8
## + practice_sport:is_first_child           2     167.8 86364 3097.9
## - is_first_child:transport_means          1     725.6 87257 3097.9
## - parent_marital_status:wkly_study_hours  6    2257.5 88789 3098.2
## + practice_sport:wkly_study_hours         4     589.5 85942 3099.0
## + gender:parent_marital_status            3     295.0 86236 3099.0
## + parent_educ:practice_sport             10    2314.6 84217 3099.0
## - parent_marital_status:transport_means   3    1496.6 88028 3099.1
## + lunch_type:parent_marital_status        3     270.6 86261 3099.2
## + parent_educ:transport_means             5     842.4 85689 3099.2
## + gender:ethnic_group                     4     451.2 86080 3099.9
## - parent_marital_status:is_first_child    3    1638.4 88170 3100.1
## - lunch_type:practice_sport               2    1356.7 87888 3100.2
## + parent_educ:lunch_type                  5     696.7 85835 3100.2
## + ethnic_group:test_prep                  4     384.9 86146 3100.4
## - parent_educ:parent_marital_status      15    5349.4 91881 3100.4
## + gender:parent_educ                      5     657.1 85874 3100.5
## + parent_educ:test_prep                   5     396.0 86135 3102.3
## + parent_marital_status:practice_sport    6     425.7 86106 3104.1
## + ethnic_group:practice_sport             8     993.6 85538 3104.2
## + ethnic_group:parent_marital_status     11    1802.0 84729 3104.6
## + ethnic_group:wkly_study_hours           8     733.7 85798 3106.0
## + parent_educ:wkly_study_hours           10    1223.2 85308 3106.6
## + ethnic_group:parent_educ               20    2369.4 84162 3118.6
## 
## Step:  AIC=3094
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:is_first_child             4    1045.7 88018 3093.1
## - lunch_type:wkly_study_hours             2     485.3 87458 3093.3
## - lunch_type:test_prep                    1     212.0 87185 3093.4
## - test_prep:is_first_child                1     279.8 87252 3093.9
## <none>                                                86973 3094.0
## - is_first_child:wkly_study_hours         2     618.8 87591 3094.2
## + gender:practice_sport                   2     441.2 86531 3095.0
## + gender:test_prep                        1     130.3 86842 3095.1
## - lunch_type:transport_means              1     467.1 87440 3095.2
## + gender:lunch_type                       1      98.8 86874 3095.3
## + gender:is_first_child                   1      77.3 86895 3095.5
## + lunch_type:is_first_child               1      67.1 86905 3095.6
## + gender:transport_means                  1      55.4 86917 3095.6
## - test_prep:wkly_study_hours              2     847.3 87820 3095.7
## + test_prep:transport_means               1      12.9 86960 3095.9
## + test_prep:practice_sport                2     266.7 86706 3096.2
## - parent_marital_status:wkly_study_hours  6    2123.6 89096 3096.2
## + test_prep:parent_marital_status         3     531.6 86441 3096.4
## + gender:wkly_study_hours                 2     221.6 86751 3096.5
## + transport_means:wkly_study_hours        2     219.6 86753 3096.5
## - ethnic_group:transport_means            4    1578.3 88551 3096.6
## - parent_educ:is_first_child              5    1897.3 88870 3096.7
## + ethnic_group:lunch_type                 4     771.2 86201 3096.8
## + practice_sport:is_first_child           2     167.3 86805 3096.9
## + practice_sport:transport_means          2     155.6 86817 3096.9
## - is_first_child:transport_means          1     764.2 87737 3097.2
## - parent_marital_status:transport_means   3    1428.3 88401 3097.6
## + gender:parent_marital_status            3     346.2 86626 3097.7
## + practice_sport:wkly_study_hours         4     637.1 86335 3097.7
## + parent_educ:transport_means             5     864.0 86109 3098.1
## + lunch_type:parent_marital_status        3     267.4 86705 3098.2
## + parent_educ:practice_sport             10    2207.6 84765 3098.8
## + parent_educ:lunch_type                  5     741.3 86231 3098.9
## + gender:ethnic_group                     4     414.5 86558 3099.2
## - parent_educ:parent_marital_status      15    5364.1 92337 3099.3
## - parent_marital_status:is_first_child    3    1684.3 88657 3099.3
## + ethnic_group:test_prep                  4     382.9 86590 3099.4
## + gender:parent_educ                      5     657.1 86316 3099.5
## - lunch_type:practice_sport               2    1466.3 88439 3099.9
## + parent_educ:test_prep                   5     353.3 86619 3101.6
## + ethnic_group:practice_sport             8    1131.7 85841 3102.3
## + parent_marital_status:practice_sport    6     408.6 86564 3103.2
## + ethnic_group:parent_marital_status     11    1849.7 85123 3103.3
## + ethnic_group:wkly_study_hours           8     736.7 86236 3105.0
## + parent_educ:wkly_study_hours           10    1160.6 85812 3106.1
## - gender                                  1    2914.0 89887 3111.4
## + ethnic_group:parent_educ               20    2455.9 84517 3117.1
## 
## Step:  AIC=3093.05
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:is_first_child + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:wkly_study_hours             2     439.6 88458 3092.0
## - lunch_type:test_prep                    1     220.6 88239 3092.5
## <none>                                                88018 3093.1
## - test_prep:is_first_child                1     327.4 88346 3093.2
## - test_prep:wkly_study_hours              2     638.7 88657 3093.3
## - lunch_type:transport_means              1     406.7 88425 3093.8
## + ethnic_group:is_first_child             4    1045.7 86973 3094.0
## - is_first_child:wkly_study_hours         2     753.2 88772 3094.1
## + gender:practice_sport                   2     412.2 87606 3094.3
## - is_first_child:transport_means          1     504.9 88523 3094.4
## + gender:test_prep                        1      91.6 87927 3094.4
## + gender:lunch_type                       1      84.2 87934 3094.5
## + gender:transport_means                  1      45.0 87973 3094.8
## + gender:is_first_child                   1      42.5 87976 3094.8
## - parent_marital_status:wkly_study_hours  6    2077.1 90095 3094.8
## + lunch_type:is_first_child               1      25.4 87993 3094.9
## + test_prep:transport_means               1       2.9 88015 3095.0
## + test_prep:practice_sport                2     279.7 87739 3095.2
## + test_prep:parent_marital_status         3     571.5 87447 3095.2
## + transport_means:wkly_study_hours        2     250.1 87768 3095.4
## + practice_sport:is_first_child           2     227.8 87790 3095.5
## - ethnic_group:transport_means            4    1651.1 89669 3096.0
## + gender:wkly_study_hours                 2     139.5 87879 3096.1
## + practice_sport:transport_means          2     136.1 87882 3096.1
## + practice_sport:wkly_study_hours         4     699.2 87319 3096.3
## - parent_educ:is_first_child              5    2019.8 90038 3096.4
## - parent_marital_status:transport_means   3    1460.3 89479 3096.8
## + parent_educ:transport_means             5     915.0 87103 3096.9
## + gender:parent_marital_status            3     278.5 87740 3097.2
## + ethnic_group:lunch_type                 4     559.4 87459 3097.3
## - parent_educ:parent_marital_status      15    5295.5 93314 3097.5
## + lunch_type:parent_marital_status        3     226.5 87792 3097.5
## + parent_educ:lunch_type                  5     815.5 87203 3097.6
## + parent_educ:practice_sport             10    2279.3 85739 3097.6
## + ethnic_group:test_prep                  4     411.9 87606 3098.3
## - lunch_type:practice_sport               2    1396.6 89415 3098.3
## + gender:ethnic_group                     4     377.8 87641 3098.5
## - parent_marital_status:is_first_child    3    1836.6 89855 3099.2
## + gender:parent_educ                      5     561.0 87457 3099.3
## + parent_educ:test_prep                   5     377.5 87641 3100.5
## + ethnic_group:practice_sport             8    1053.2 86965 3101.9
## + parent_marital_status:practice_sport    6     283.5 87735 3103.2
## + ethnic_group:wkly_study_hours           8     783.8 87235 3103.8
## + ethnic_group:parent_marital_status     11    1528.1 86490 3104.7
## + parent_educ:wkly_study_hours           10    1203.3 86815 3104.9
## - gender                                  1    3194.3 91213 3112.1
## + ethnic_group:parent_educ               20    2547.3 85471 3115.7
## 
## Step:  AIC=3091.99
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:test_prep                    1     183.8 88642 3091.2
## <none>                                                88458 3092.0
## - test_prep:is_first_child                1     353.8 88812 3092.3
## - lunch_type:transport_means              1     389.2 88847 3092.6
## - test_prep:wkly_study_hours              2     693.4 89151 3092.6
## - parent_marital_status:wkly_study_hours  6    1937.5 90395 3092.8
## + lunch_type:wkly_study_hours             2     439.6 88018 3093.1
## - is_first_child:wkly_study_hours         2     763.2 89221 3093.1
## + ethnic_group:is_first_child             4    1000.0 87458 3093.3
## + gender:test_prep                        1     103.6 88354 3093.3
## + gender:practice_sport                   2     395.2 88063 3093.3
## + gender:lunch_type                       1      74.0 88384 3093.5
## - is_first_child:transport_means          1     556.8 89015 3093.7
## + gender:is_first_child                   1      40.5 88417 3093.7
## + gender:transport_means                  1      29.5 88428 3093.8
## + test_prep:practice_sport                2     322.7 88135 3093.8
## + lunch_type:is_first_child               1      16.5 88441 3093.9
## + test_prep:transport_means               1       1.5 88456 3094.0
## + transport_means:wkly_study_hours        2     289.0 88169 3094.1
## + test_prep:parent_marital_status         3     573.8 87884 3094.2
## + practice_sport:is_first_child           2     234.2 88224 3094.4
## - ethnic_group:transport_means            4    1593.9 90052 3094.5
## - parent_educ:is_first_child              5    1983.0 90441 3095.1
## + practice_sport:transport_means          2     128.9 88329 3095.1
## + gender:wkly_study_hours                 2     103.0 88355 3095.3
## + parent_educ:transport_means             5     988.3 87470 3095.4
## - parent_marital_status:transport_means   3    1439.2 89897 3095.5
## + practice_sport:wkly_study_hours         4     664.7 87793 3095.5
## + gender:parent_marital_status            3     332.0 88126 3095.8
## + parent_educ:practice_sport             10    2350.0 86108 3096.1
## + lunch_type:parent_marital_status        3     206.8 88251 3096.6
## + ethnic_group:lunch_type                 4     504.4 87953 3096.6
## - parent_educ:parent_marital_status      15    5358.7 93817 3096.7
## + ethnic_group:test_prep                  4     423.2 88035 3097.2
## + parent_educ:lunch_type                  5     709.1 87749 3097.2
## - lunch_type:practice_sport               2    1411.9 89870 3097.3
## + gender:ethnic_group                     4     346.1 88112 3097.7
## + gender:parent_educ                      5     616.5 87841 3097.9
## - parent_marital_status:is_first_child    3    1837.0 90295 3098.1
## + parent_educ:test_prep                   5     386.1 88072 3099.4
## + ethnic_group:practice_sport             8    1034.5 87423 3101.1
## + parent_marital_status:practice_sport    6     290.1 88168 3102.1
## + ethnic_group:wkly_study_hours           8     803.7 87654 3102.6
## + ethnic_group:parent_marital_status     11    1478.6 86979 3104.1
## + parent_educ:wkly_study_hours           10    1132.5 87325 3104.4
## - gender                                  1    3238.9 91697 3111.2
## + ethnic_group:parent_educ               20    2566.2 85892 3114.6
## 
## Step:  AIC=3091.22
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:practice_sport + lunch_type:transport_means + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## <none>                                                88642 3091.2
## - test_prep:is_first_child                1     340.8 88982 3091.5
## - lunch_type:transport_means              1     343.0 88985 3091.5
## - test_prep:wkly_study_hours              2     699.0 89341 3091.8
## + lunch_type:test_prep                    1     183.8 88458 3092.0
## - parent_marital_status:wkly_study_hours  6    1959.2 90601 3092.1
## + gender:test_prep                        1     118.0 88524 3092.4
## + ethnic_group:is_first_child             4    1007.9 87634 3092.5
## + lunch_type:wkly_study_hours             2     402.8 88239 3092.5
## + gender:practice_sport                   2     399.7 88242 3092.6
## - is_first_child:wkly_study_hours         2     806.1 89448 3092.6
## - is_first_child:transport_means          1     504.9 89147 3092.6
## + gender:lunch_type                       1      94.2 88547 3092.6
## + gender:is_first_child                   1      46.8 88595 3092.9
## + gender:transport_means                  1      33.6 88608 3093.0
## + test_prep:practice_sport                2     332.6 88309 3093.0
## + lunch_type:is_first_child               1      14.2 88627 3093.1
## + test_prep:transport_means               1       0.9 88641 3093.2
## + test_prep:parent_marital_status         3     572.8 88069 3093.4
## + transport_means:wkly_study_hours        2     262.7 88379 3093.5
## + practice_sport:is_first_child           2     245.6 88396 3093.6
## - ethnic_group:transport_means            4    1620.7 90262 3093.9
## - parent_educ:is_first_child              5    1937.1 90579 3094.0
## + practice_sport:transport_means          2     152.2 88490 3094.2
## + gender:wkly_study_hours                 2     104.4 88537 3094.5
## + practice_sport:wkly_study_hours         4     694.6 87947 3094.6
## + parent_educ:transport_means             5     980.6 87661 3094.7
## - parent_marital_status:transport_means   3    1457.2 90099 3094.8
## + gender:parent_marital_status            3     336.0 88306 3095.0
## - parent_educ:parent_marital_status      15    5267.7 93909 3095.3
## + parent_educ:practice_sport             10    2356.5 86285 3095.3
## + ethnic_group:lunch_type                 4     527.6 88114 3095.7
## + lunch_type:parent_marital_status        3     190.8 88451 3095.9
## - lunch_type:practice_sport               2    1378.2 90020 3096.3
## + ethnic_group:test_prep                  4     405.7 88236 3096.5
## + parent_educ:lunch_type                  5     676.9 87965 3096.7
## + gender:ethnic_group                     4     349.9 88292 3096.9
## + gender:parent_educ                      5     646.5 87995 3096.9
## - parent_marital_status:is_first_child    3    1860.2 90502 3097.5
## + parent_educ:test_prep                   5     412.2 88229 3098.5
## + ethnic_group:practice_sport             8    1081.3 87560 3100.0
## + parent_marital_status:practice_sport    6     299.4 88342 3101.2
## + ethnic_group:wkly_study_hours           8     857.1 87785 3101.5
## + parent_educ:wkly_study_hours           10    1206.0 87436 3103.1
## + ethnic_group:parent_marital_status     11    1444.1 87198 3103.5
## - gender                                  1    3294.9 91937 3110.8
## + ethnic_group:parent_educ               20    2571.4 86070 3113.8
summary(stepwise_model_math)
## 
## Call:
## lm(formula = math_score ~ gender + ethnic_group + parent_educ + 
##     lunch_type + test_prep + parent_marital_status + practice_sport + 
##     is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:practice_sport + lunch_type:transport_means + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours, 
##     data = df_4_mdl_math)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -48.225  -8.356   0.435   8.408  29.970 
## 
## Coefficients:
##                                                           Estimate Std. Error
## (Intercept)                                                43.4922     7.6094
## gendermale                                                  5.0562     1.1468
## ethnic_groupgroup B                                         3.1099     3.8855
## ethnic_groupgroup C                                         4.7867     3.5363
## ethnic_groupgroup D                                         4.4789     3.6141
## ethnic_groupgroup E                                        19.5605     4.0197
## parent_educbachelor's degree                               22.6142     6.3793
## parent_educhigh school                                    -11.9676     5.2257
## parent_educmaster's degree                                 -1.9384     7.3940
## parent_educsome college                                     0.8824     5.2535
## parent_educsome high school                                 1.6696     5.2602
## lunch_typestandard                                          5.7052     3.8861
## test_prepnone                                              -1.1067     3.0821
## parent_marital_statusmarried                                9.7202     5.4642
## parent_marital_statussingle                                 3.7791     6.1207
## parent_marital_statuswidowed                               29.2538    21.3074
## practice_sportregularly                                    -4.2709     3.3825
## practice_sportsometimes                                    -6.0415     3.2607
## is_first_childyes                                          12.5726     5.4684
## transport_meansschool_bus                                   5.2495     5.3829
## wkly_study_hours> 10                                       -4.8803     6.2686
## wkly_study_hours10-May                                      4.6584     4.6603
## ethnic_groupgroup B:transport_meansschool_bus              -4.3677     4.8098
## ethnic_groupgroup C:transport_meansschool_bus              -7.7457     4.4977
## ethnic_groupgroup D:transport_meansschool_bus              -0.9133     4.5777
## ethnic_groupgroup E:transport_meansschool_bus             -10.3518     5.0390
## parent_educbachelor's degree:parent_marital_statusmarried -18.4745     6.5736
## parent_educhigh school:parent_marital_statusmarried         0.7418     4.8751
## parent_educmaster's degree:parent_marital_statusmarried     1.1993     6.6521
## parent_educsome college:parent_marital_statusmarried       -7.4232     4.9354
## parent_educsome high school:parent_marital_statusmarried   -8.2283     4.9536
## parent_educbachelor's degree:parent_marital_statussingle  -23.6304     7.4269
## parent_educhigh school:parent_marital_statussingle          1.7141     5.5986
## parent_educmaster's degree:parent_marital_statussingle     -0.6344     7.3500
## parent_educsome college:parent_marital_statussingle       -11.5881     5.6728
## parent_educsome high school:parent_marital_statussingle   -11.5407     5.5591
## parent_educbachelor's degree:parent_marital_statuswidowed -33.5004    17.3280
## parent_educhigh school:parent_marital_statuswidowed       -46.5554    20.4448
## parent_educmaster's degree:parent_marital_statuswidowed   -48.9590    29.6690
## parent_educsome college:parent_marital_statuswidowed      -15.7099    19.0668
## parent_educsome high school:parent_marital_statuswidowed  -19.2638    19.6446
## parent_educbachelor's degree:is_first_childyes             -3.3589     4.3330
## parent_educhigh school:is_first_childyes                    8.9969     3.8002
## parent_educmaster's degree:is_first_childyes                4.7183     5.6364
## parent_educsome college:is_first_childyes                   6.6947     3.7542
## parent_educsome high school:is_first_childyes               2.0436     3.7438
## lunch_typestandard:practice_sportregularly                  8.4203     4.1608
## lunch_typestandard:practice_sportsometimes                 11.3662     4.0244
## lunch_typestandard:transport_meansschool_bus               -3.4368     2.4159
## test_prepnone:is_first_childyes                            -3.6884     2.6012
## test_prepnone:wkly_study_hours> 10                         -6.2865     3.6457
## test_prepnone:wkly_study_hours10-May                       -0.1976     2.8984
## parent_marital_statusmarried:is_first_childyes             -8.7047     3.9485
## parent_marital_statussingle:is_first_childyes              -1.9060     4.3893
## parent_marital_statuswidowed:is_first_childyes             13.7975    13.4714
## parent_marital_statusmarried:transport_meansschool_bus      7.2707     3.3639
## parent_marital_statussingle:transport_meansschool_bus       2.4715     3.7983
## parent_marital_statuswidowed:transport_meansschool_bus    -14.6085    12.8542
## parent_marital_statusmarried:wkly_study_hours> 10          11.6354     5.1480
## parent_marital_statussingle:wkly_study_hours> 10           18.6339     5.7474
## parent_marital_statuswidowed:wkly_study_hours> 10          11.9898    16.7894
## parent_marital_statusmarried:wkly_study_hours10-May         2.1127     3.7866
## parent_marital_statussingle:wkly_study_hours10-May          5.6965     4.2936
## parent_marital_statuswidowed:wkly_study_hours10-May        11.8849    14.3211
## is_first_childyes:transport_meansschool_bus                -4.4000     2.5494
## is_first_childyes:wkly_study_hours> 10                     -0.6479     3.7705
## is_first_childyes:wkly_study_hours10-May                   -5.6646     2.8793
##                                                           t value Pr(>|t|)    
## (Intercept)                                                 5.716 1.84e-08 ***
## gendermale                                                  4.409 1.26e-05 ***
## ethnic_groupgroup B                                         0.800 0.423863    
## ethnic_groupgroup C                                         1.354 0.176457    
## ethnic_groupgroup D                                         1.239 0.215799    
## ethnic_groupgroup E                                         4.866 1.51e-06 ***
## parent_educbachelor's degree                                3.545 0.000428 ***
## parent_educhigh school                                     -2.290 0.022411 *  
## parent_educmaster's degree                                 -0.262 0.793302    
## parent_educsome college                                     0.168 0.866672    
## parent_educsome high school                                 0.317 0.751071    
## lunch_typestandard                                          1.468 0.142671    
## test_prepnone                                              -0.359 0.719670    
## parent_marital_statusmarried                                1.779 0.075838 .  
## parent_marital_statussingle                                 0.617 0.537217    
## parent_marital_statuswidowed                                1.373 0.170360    
## practice_sportregularly                                    -1.263 0.207275    
## practice_sportsometimes                                    -1.853 0.064470 .  
## is_first_childyes                                           2.299 0.021890 *  
## transport_meansschool_bus                                   0.975 0.329901    
## wkly_study_hours> 10                                       -0.779 0.436602    
## wkly_study_hours10-May                                      1.000 0.317963    
## ethnic_groupgroup B:transport_meansschool_bus              -0.908 0.364253    
## ethnic_groupgroup C:transport_meansschool_bus              -1.722 0.085632 .  
## ethnic_groupgroup D:transport_meansschool_bus              -0.200 0.841936    
## ethnic_groupgroup E:transport_meansschool_bus              -2.054 0.040440 *  
## parent_educbachelor's degree:parent_marital_statusmarried  -2.810 0.005133 ** 
## parent_educhigh school:parent_marital_statusmarried         0.152 0.879115    
## parent_educmaster's degree:parent_marital_statusmarried     0.180 0.856998    
## parent_educsome college:parent_marital_statusmarried       -1.504 0.133168    
## parent_educsome high school:parent_marital_statusmarried   -1.661 0.097298 .  
## parent_educbachelor's degree:parent_marital_statussingle   -3.182 0.001551 ** 
## parent_educhigh school:parent_marital_statussingle          0.306 0.759606    
## parent_educmaster's degree:parent_marital_statussingle     -0.086 0.931250    
## parent_educsome college:parent_marital_statussingle        -2.043 0.041580 *  
## parent_educsome high school:parent_marital_statussingle    -2.076 0.038380 *  
## parent_educbachelor's degree:parent_marital_statuswidowed  -1.933 0.053737 .  
## parent_educhigh school:parent_marital_statuswidowed        -2.277 0.023182 *  
## parent_educmaster's degree:parent_marital_statuswidowed    -1.650 0.099508 .  
## parent_educsome college:parent_marital_statuswidowed       -0.824 0.410350    
## parent_educsome high school:parent_marital_statuswidowed   -0.981 0.327238    
## parent_educbachelor's degree:is_first_childyes             -0.775 0.438573    
## parent_educhigh school:is_first_childyes                    2.368 0.018271 *  
## parent_educmaster's degree:is_first_childyes                0.837 0.402905    
## parent_educsome college:is_first_childyes                   1.783 0.075121 .  
## parent_educsome high school:is_first_childyes               0.546 0.585404    
## lunch_typestandard:practice_sportregularly                  2.024 0.043509 *  
## lunch_typestandard:practice_sportsometimes                  2.824 0.004918 ** 
## lunch_typestandard:transport_meansschool_bus               -1.423 0.155457    
## test_prepnone:is_first_childyes                            -1.418 0.156801    
## test_prepnone:wkly_study_hours> 10                         -1.724 0.085236 .  
## test_prepnone:wkly_study_hours10-May                       -0.068 0.945661    
## parent_marital_statusmarried:is_first_childyes             -2.205 0.027922 *  
## parent_marital_statussingle:is_first_childyes              -0.434 0.664285    
## parent_marital_statuswidowed:is_first_childyes              1.024 0.306211    
## parent_marital_statusmarried:transport_meansschool_bus      2.161 0.031117 *  
## parent_marital_statussingle:transport_meansschool_bus       0.651 0.515535    
## parent_marital_statuswidowed:transport_meansschool_bus     -1.136 0.256279    
## parent_marital_statusmarried:wkly_study_hours> 10           2.260 0.024220 *  
## parent_marital_statussingle:wkly_study_hours> 10            3.242 0.001262 ** 
## parent_marital_statuswidowed:wkly_study_hours> 10           0.714 0.475465    
## parent_marital_statusmarried:wkly_study_hours10-May         0.558 0.577124    
## parent_marital_statussingle:wkly_study_hours10-May          1.327 0.185170    
## parent_marital_statuswidowed:wkly_study_hours10-May         0.830 0.406980    
## is_first_childyes:transport_meansschool_bus                -1.726 0.084951 .  
## is_first_childyes:wkly_study_hours> 10                     -0.172 0.863627    
## is_first_childyes:wkly_study_hours10-May                   -1.967 0.049669 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.02 on 523 degrees of freedom
## Multiple R-squared:  0.4207, Adjusted R-squared:  0.3476 
## F-statistic: 5.755 on 66 and 523 DF,  p-value: < 2.2e-16

REading Score

df_4_mdl_read=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,reading_score)
full_fit_read=lm(reading_score ~ .^2,data=df_4_mdl_read)
summary(full_fit_read)
## 
## Call:
## lm(formula = reading_score ~ .^2, data = df_4_mdl_read)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -34.758  -7.294   0.000   7.418  27.742 
## 
## Coefficients: (4 not defined because of singularities)
##                                                             Estimate Std. Error
## (Intercept)                                                81.321731  17.167189
## gendermale                                                -12.452051   8.746220
## ethnic_groupgroup B                                       -22.239861  14.760619
## ethnic_groupgroup C                                       -29.866442  13.925159
## ethnic_groupgroup D                                       -14.526414  15.158345
## ethnic_groupgroup E                                       -12.302699  14.206212
## parent_educbachelor's degree                               33.009059  15.519735
## parent_educhigh school                                     10.568006  12.847471
## parent_educmaster's degree                                -24.461817  21.208891
## parent_educsome college                                    -8.316968  12.606066
## parent_educsome high school                                -4.455992  12.227987
## lunch_typestandard                                          2.962788   8.683223
## test_prepnone                                             -21.345506   9.059903
## parent_marital_statusmarried                               16.095657  11.535602
## parent_marital_statussingle                                 5.120602  13.883607
## parent_marital_statuswidowed                               30.884374  41.015667
## practice_sportregularly                                   -22.428022  13.810663
## practice_sportsometimes                                   -19.634669  13.740867
## is_first_childyes                                          16.375726   9.948217
## transport_meansschool_bus                                  -1.212990   8.806349
## wkly_study_hours> 10                                      -17.887902  13.565927
## wkly_study_hours10-May                                      6.195369  10.901941
## gendermale:ethnic_groupgroup B                              7.922999   5.540120
## gendermale:ethnic_groupgroup C                             12.191147   5.327795
## gendermale:ethnic_groupgroup D                              8.192752   5.292503
## gendermale:ethnic_groupgroup E                              9.251399   5.868168
## gendermale:parent_educbachelor's degree                    -2.815989   4.660163
## gendermale:parent_educhigh school                           0.610374   3.800446
## gendermale:parent_educmaster's degree                       7.279615   6.524814
## gendermale:parent_educsome college                         -4.141922   3.991004
## gendermale:parent_educsome high school                      1.008352   3.920233
## gendermale:lunch_typestandard                              -1.073739   2.722340
## gendermale:test_prepnone                                    0.251653   2.713118
## gendermale:parent_marital_statusmarried                    -0.523193   3.867655
## gendermale:parent_marital_statussingle                     -1.745302   4.384747
## gendermale:parent_marital_statuswidowed                     1.627846  18.986441
## gendermale:practice_sportregularly                         -4.310235   4.610325
## gendermale:practice_sportsometimes                         -3.516087   4.634508
## gendermale:is_first_childyes                                3.360372   2.847909
## gendermale:transport_meansschool_bus                       -0.351231   2.632552
## gendermale:wkly_study_hours> 10                            -4.536157   4.129918
## gendermale:wkly_study_hours10-May                          -1.585990   3.132127
## ethnic_groupgroup B:parent_educbachelor's degree           -3.324954  12.924044
## ethnic_groupgroup C:parent_educbachelor's degree           -1.783597  12.903276
## ethnic_groupgroup D:parent_educbachelor's degree           -4.193155  12.805839
## ethnic_groupgroup E:parent_educbachelor's degree          -11.352581  14.573901
## ethnic_groupgroup B:parent_educhigh school                -15.455925   8.091351
## ethnic_groupgroup C:parent_educhigh school                 -8.942855   7.776991
## ethnic_groupgroup D:parent_educhigh school                 -7.859495   7.906714
## ethnic_groupgroup E:parent_educhigh school                 -9.368700   8.805485
## ethnic_groupgroup B:parent_educmaster's degree             19.405920  15.527488
## ethnic_groupgroup C:parent_educmaster's degree              4.673731  14.422492
## ethnic_groupgroup D:parent_educmaster's degree             12.168775  14.651954
## ethnic_groupgroup E:parent_educmaster's degree             14.049007  15.416565
## ethnic_groupgroup B:parent_educsome college                 4.664900   8.948253
## ethnic_groupgroup C:parent_educsome college                 8.349426   8.446297
## ethnic_groupgroup D:parent_educsome college                11.079460   8.797228
## ethnic_groupgroup E:parent_educsome college                 8.211551   8.893668
## ethnic_groupgroup B:parent_educsome high school           -11.966506   8.576569
## ethnic_groupgroup C:parent_educsome high school            -4.495760   8.047085
## ethnic_groupgroup D:parent_educsome high school            -3.780939   8.099992
## ethnic_groupgroup E:parent_educsome high school             4.417092   8.696931
## ethnic_groupgroup B:lunch_typestandard                      5.652071   5.760897
## ethnic_groupgroup C:lunch_typestandard                     10.226437   5.587239
## ethnic_groupgroup D:lunch_typestandard                      8.972876   5.499776
## ethnic_groupgroup E:lunch_typestandard                      1.828807   6.373559
## ethnic_groupgroup B:test_prepnone                           5.358082   5.877498
## ethnic_groupgroup C:test_prepnone                          10.226148   5.513504
## ethnic_groupgroup D:test_prepnone                           7.509603   5.524539
## ethnic_groupgroup E:test_prepnone                          13.877806   6.013663
## ethnic_groupgroup B:parent_marital_statusmarried            7.666966   7.934987
## ethnic_groupgroup C:parent_marital_statusmarried            1.502948   7.306752
## ethnic_groupgroup D:parent_marital_statusmarried           -9.884703   7.206665
## ethnic_groupgroup E:parent_marital_statusmarried           -0.914626   7.973170
## ethnic_groupgroup B:parent_marital_statussingle            18.560281   9.394771
## ethnic_groupgroup C:parent_marital_statussingle             7.986241   8.882343
## ethnic_groupgroup D:parent_marital_statussingle             3.213487   8.582960
## ethnic_groupgroup E:parent_marital_statussingle            14.967904   9.892795
## ethnic_groupgroup B:parent_marital_statuswidowed           50.612530 105.115426
## ethnic_groupgroup C:parent_marital_statuswidowed           78.991045  85.429965
## ethnic_groupgroup D:parent_marital_statuswidowed            4.650894  86.120208
## ethnic_groupgroup E:parent_marital_statuswidowed                  NA         NA
## ethnic_groupgroup B:practice_sportregularly                14.613295  10.525698
## ethnic_groupgroup C:practice_sportregularly                14.627286  10.430812
## ethnic_groupgroup D:practice_sportregularly                12.114331  11.643524
## ethnic_groupgroup E:practice_sportregularly                15.486520  10.659168
## ethnic_groupgroup B:practice_sportsometimes                14.385211  11.228160
## ethnic_groupgroup C:practice_sportsometimes                22.578975  10.921110
## ethnic_groupgroup D:practice_sportsometimes                13.257823  12.039573
## ethnic_groupgroup E:practice_sportsometimes                14.799736  10.976620
## ethnic_groupgroup B:is_first_childyes                       7.019423   5.832717
## ethnic_groupgroup C:is_first_childyes                       0.945600   5.502186
## ethnic_groupgroup D:is_first_childyes                      -0.578091   5.565974
## ethnic_groupgroup E:is_first_childyes                       0.006724   6.269137
## ethnic_groupgroup B:transport_meansschool_bus              -9.549492   5.835934
## ethnic_groupgroup C:transport_meansschool_bus             -12.156811   5.388780
## ethnic_groupgroup D:transport_meansschool_bus              -3.839999   5.383422
## ethnic_groupgroup E:transport_meansschool_bus             -11.722753   6.354914
## ethnic_groupgroup B:wkly_study_hours> 10                   -8.400227   9.935104
## ethnic_groupgroup C:wkly_study_hours> 10                   -0.687654   9.811241
## ethnic_groupgroup D:wkly_study_hours> 10                    0.263262   9.797612
## ethnic_groupgroup E:wkly_study_hours> 10                   -2.759617  10.673194
## ethnic_groupgroup B:wkly_study_hours10-May                 -7.860645   8.344055
## ethnic_groupgroup C:wkly_study_hours10-May                 -2.433650   8.164758
## ethnic_groupgroup D:wkly_study_hours10-May                 -2.347630   8.302701
## ethnic_groupgroup E:wkly_study_hours10-May                 -6.220986   8.939387
## parent_educbachelor's degree:lunch_typestandard             0.537231   5.014512
## parent_educhigh school:lunch_typestandard                   0.798236   4.046623
## parent_educmaster's degree:lunch_typestandard               6.644511   7.416722
## parent_educsome college:lunch_typestandard                  3.328751   4.079308
## parent_educsome high school:lunch_typestandard              5.530921   4.225656
## parent_educbachelor's degree:test_prepnone                 -2.906807   4.626773
## parent_educhigh school:test_prepnone                        2.313360   4.431222
## parent_educmaster's degree:test_prepnone                    0.511485   7.888189
## parent_educsome college:test_prepnone                      -3.095198   4.153258
## parent_educsome high school:test_prepnone                   2.618495   4.016780
## parent_educbachelor's degree:parent_marital_statusmarried -18.253458   8.257834
## parent_educhigh school:parent_marital_statusmarried         3.996656   5.807660
## parent_educmaster's degree:parent_marital_statusmarried     0.758405   8.402414
## parent_educsome college:parent_marital_statusmarried       -7.340772   5.719024
## parent_educsome high school:parent_marital_statusmarried   -4.263094   5.636000
## parent_educbachelor's degree:parent_marital_statussingle  -16.758528   8.901756
## parent_educhigh school:parent_marital_statussingle          8.616682   6.344144
## parent_educmaster's degree:parent_marital_statussingle      0.012577   8.969310
## parent_educsome college:parent_marital_statussingle        -5.727081   6.369453
## parent_educsome high school:parent_marital_statussingle    -1.033222   6.292098
## parent_educbachelor's degree:parent_marital_statuswidowed -21.688307  87.516115
## parent_educhigh school:parent_marital_statuswidowed       -57.550419  96.291731
## parent_educmaster's degree:parent_marital_statuswidowed   -77.367781  50.441787
## parent_educsome college:parent_marital_statuswidowed      -60.045162  63.244771
## parent_educsome high school:parent_marital_statuswidowed  -37.108747  75.801849
## parent_educbachelor's degree:practice_sportregularly       -3.662981   8.525723
## parent_educhigh school:practice_sportregularly            -14.710426   7.337095
## parent_educmaster's degree:practice_sportregularly          1.377177  10.367956
## parent_educsome college:practice_sportregularly            -0.382685   7.461303
## parent_educsome high school:practice_sportregularly        -3.964045   7.205456
## parent_educbachelor's degree:practice_sportsometimes      -12.591005   8.181090
## parent_educhigh school:practice_sportsometimes            -11.930485   6.949111
## parent_educmaster's degree:practice_sportsometimes          6.527368   8.636835
## parent_educsome college:practice_sportsometimes             1.040653   7.180635
## parent_educsome high school:practice_sportsometimes         1.496483   6.751679
## parent_educbachelor's degree:is_first_childyes              4.788458   5.062901
## parent_educhigh school:is_first_childyes                    6.532806   4.321769
## parent_educmaster's degree:is_first_childyes                6.212508   7.559206
## parent_educsome college:is_first_childyes                   9.548352   4.220353
## parent_educsome high school:is_first_childyes               4.792705   4.250326
## parent_educbachelor's degree:transport_meansschool_bus      0.906739   5.054249
## parent_educhigh school:transport_meansschool_bus            3.388782   4.035129
## parent_educmaster's degree:transport_meansschool_bus        4.816803   6.221602
## parent_educsome college:transport_meansschool_bus           3.654650   4.108899
## parent_educsome high school:transport_meansschool_bus       6.032445   4.180954
## parent_educbachelor's degree:wkly_study_hours> 10          -8.191880   7.456993
## parent_educhigh school:wkly_study_hours> 10                -8.343145   6.207418
## parent_educmaster's degree:wkly_study_hours> 10            -1.790263  13.431842
## parent_educsome college:wkly_study_hours> 10               -5.998216   6.248173
## parent_educsome high school:wkly_study_hours> 10           -6.744473   6.363801
## parent_educbachelor's degree:wkly_study_hours10-May        -1.946279   5.182903
## parent_educhigh school:wkly_study_hours10-May             -10.690295   4.832196
## parent_educmaster's degree:wkly_study_hours10-May          -1.124984   6.910172
## parent_educsome college:wkly_study_hours10-May             -2.915727   4.920451
## parent_educsome high school:wkly_study_hours10-May         -8.675554   5.191456
## lunch_typestandard:test_prepnone                           -3.365201   3.035153
## lunch_typestandard:parent_marital_statusmarried            -7.902908   3.971499
## lunch_typestandard:parent_marital_statussingle             -3.707488   4.598623
## lunch_typestandard:parent_marital_statuswidowed             9.372773  78.604395
## lunch_typestandard:practice_sportregularly                  6.988929   5.235054
## lunch_typestandard:practice_sportsometimes                 10.284128   5.046396
## lunch_typestandard:is_first_childyes                       -3.701755   3.075286
## lunch_typestandard:transport_meansschool_bus               -3.696061   2.822109
## lunch_typestandard:wkly_study_hours> 10                     7.910873   4.306472
## lunch_typestandard:wkly_study_hours10-May                  -0.616925   3.221350
## test_prepnone:parent_marital_statusmarried                  3.767046   4.039735
## test_prepnone:parent_marital_statussingle                  -0.269557   4.650957
## test_prepnone:parent_marital_statuswidowed                -33.676919  41.067330
## test_prepnone:practice_sportregularly                       2.975412   5.049660
## test_prepnone:practice_sportsometimes                       4.627924   4.948802
## test_prepnone:is_first_childyes                             1.185331   3.047862
## test_prepnone:transport_meansschool_bus                     1.799887   2.771281
## test_prepnone:wkly_study_hours> 10                         -2.777623   4.350100
## test_prepnone:wkly_study_hours10-May                        1.550628   3.433108
## parent_marital_statusmarried:practice_sportregularly        3.293520   6.491421
## parent_marital_statussingle:practice_sportregularly        -4.424243   8.489011
## parent_marital_statuswidowed:practice_sportregularly       -6.906882  83.123661
## parent_marital_statusmarried:practice_sportsometimes        1.290178   6.401773
## parent_marital_statussingle:practice_sportsometimes        -4.334220   8.299021
## parent_marital_statuswidowed:practice_sportsometimes              NA         NA
## parent_marital_statusmarried:is_first_childyes            -17.146416   4.775198
## parent_marital_statussingle:is_first_childyes              -8.538880   5.292427
## parent_marital_statuswidowed:is_first_childyes             21.917582  29.457760
## parent_marital_statusmarried:transport_meansschool_bus      4.369244   3.943480
## parent_marital_statussingle:transport_meansschool_bus      -1.084605   4.494112
## parent_marital_statuswidowed:transport_meansschool_bus    -14.288412  19.143923
## parent_marital_statusmarried:wkly_study_hours> 10          21.137631   6.160491
## parent_marital_statussingle:wkly_study_hours> 10           27.104463   6.851117
## parent_marital_statuswidowed:wkly_study_hours> 10                 NA         NA
## parent_marital_statusmarried:wkly_study_hours10-May         3.638193   4.522464
## parent_marital_statussingle:wkly_study_hours10-May          4.406511   4.994941
## parent_marital_statuswidowed:wkly_study_hours10-May               NA         NA
## practice_sportregularly:is_first_childyes                  -3.848217   5.864087
## practice_sportsometimes:is_first_childyes                  -6.246496   5.721937
## practice_sportregularly:transport_meansschool_bus           8.897678   4.900075
## practice_sportsometimes:transport_meansschool_bus           5.610130   4.755946
## practice_sportregularly:wkly_study_hours> 10                4.200015   6.947009
## practice_sportsometimes:wkly_study_hours> 10                3.936511   6.813953
## practice_sportregularly:wkly_study_hours10-May              7.801823   5.346218
## practice_sportsometimes:wkly_study_hours10-May              0.374090   5.271160
## is_first_childyes:transport_meansschool_bus                -1.537098   2.982819
## is_first_childyes:wkly_study_hours> 10                      2.206912   4.484172
## is_first_childyes:wkly_study_hours10-May                   -2.954512   3.384923
## transport_meansschool_bus:wkly_study_hours> 10              0.704788   4.309112
## transport_meansschool_bus:wkly_study_hours10-May            2.548938   3.111517
##                                                           t value Pr(>|t|)    
## (Intercept)                                                 4.737 3.06e-06 ***
## gendermale                                                 -1.424 0.155346    
## ethnic_groupgroup B                                        -1.507 0.132711    
## ethnic_groupgroup C                                        -2.145 0.032599 *  
## ethnic_groupgroup D                                        -0.958 0.338510    
## ethnic_groupgroup E                                        -0.866 0.387028    
## parent_educbachelor's degree                                2.127 0.034066 *  
## parent_educhigh school                                      0.823 0.411262    
## parent_educmaster's degree                                 -1.153 0.249476    
## parent_educsome college                                    -0.660 0.509805    
## parent_educsome high school                                -0.364 0.715753    
## lunch_typestandard                                          0.341 0.733134    
## test_prepnone                                              -2.356 0.018974 *  
## parent_marital_statusmarried                                1.395 0.163733    
## parent_marital_statussingle                                 0.369 0.712463    
## parent_marital_statuswidowed                                0.753 0.451919    
## practice_sportregularly                                    -1.624 0.105206    
## practice_sportsometimes                                    -1.429 0.153841    
## is_first_childyes                                           1.646 0.100564    
## transport_meansschool_bus                                  -0.138 0.890518    
## wkly_study_hours> 10                                       -1.319 0.188094    
## wkly_study_hours10-May                                      0.568 0.570177    
## gendermale:ethnic_groupgroup B                              1.430 0.153500    
## gendermale:ethnic_groupgroup C                              2.288 0.022669 *  
## gendermale:ethnic_groupgroup D                              1.548 0.122450    
## gendermale:ethnic_groupgroup E                              1.577 0.115727    
## gendermale:parent_educbachelor's degree                    -0.604 0.546023    
## gendermale:parent_educhigh school                           0.161 0.872488    
## gendermale:parent_educmaster's degree                       1.116 0.265258    
## gendermale:parent_educsome college                         -1.038 0.300011    
## gendermale:parent_educsome high school                      0.257 0.797149    
## gendermale:lunch_typestandard                              -0.394 0.693492    
## gendermale:test_prepnone                                    0.093 0.926147    
## gendermale:parent_marital_statusmarried                    -0.135 0.892466    
## gendermale:parent_marital_statussingle                     -0.398 0.690823    
## gendermale:parent_marital_statuswidowed                     0.086 0.931720    
## gendermale:practice_sportregularly                         -0.935 0.350424    
## gendermale:practice_sportsometimes                         -0.759 0.448513    
## gendermale:is_first_childyes                                1.180 0.238755    
## gendermale:transport_meansschool_bus                       -0.133 0.893933    
## gendermale:wkly_study_hours> 10                            -1.098 0.272735    
## gendermale:wkly_study_hours10-May                          -0.506 0.612894    
## ethnic_groupgroup B:parent_educbachelor's degree           -0.257 0.797109    
## ethnic_groupgroup C:parent_educbachelor's degree           -0.138 0.890133    
## ethnic_groupgroup D:parent_educbachelor's degree           -0.327 0.743513    
## ethnic_groupgroup E:parent_educbachelor's degree           -0.779 0.436480    
## ethnic_groupgroup B:parent_educhigh school                 -1.910 0.056857 .  
## ethnic_groupgroup C:parent_educhigh school                 -1.150 0.250898    
## ethnic_groupgroup D:parent_educhigh school                 -0.994 0.320837    
## ethnic_groupgroup E:parent_educhigh school                 -1.064 0.288016    
## ethnic_groupgroup B:parent_educmaster's degree              1.250 0.212144    
## ethnic_groupgroup C:parent_educmaster's degree              0.324 0.746071    
## ethnic_groupgroup D:parent_educmaster's degree              0.831 0.406761    
## ethnic_groupgroup E:parent_educmaster's degree              0.911 0.362714    
## ethnic_groupgroup B:parent_educsome college                 0.521 0.602445    
## ethnic_groupgroup C:parent_educsome college                 0.989 0.323517    
## ethnic_groupgroup D:parent_educsome college                 1.259 0.208643    
## ethnic_groupgroup E:parent_educsome college                 0.923 0.356431    
## ethnic_groupgroup B:parent_educsome high school            -1.395 0.163747    
## ethnic_groupgroup C:parent_educsome high school            -0.559 0.576705    
## ethnic_groupgroup D:parent_educsome high school            -0.467 0.640921    
## ethnic_groupgroup E:parent_educsome high school             0.508 0.611822    
## ethnic_groupgroup B:lunch_typestandard                      0.981 0.327158    
## ethnic_groupgroup C:lunch_typestandard                      1.830 0.067979 .  
## ethnic_groupgroup D:lunch_typestandard                      1.631 0.103607    
## ethnic_groupgroup E:lunch_typestandard                      0.287 0.774316    
## ethnic_groupgroup B:test_prepnone                           0.912 0.362539    
## ethnic_groupgroup C:test_prepnone                           1.855 0.064401 .  
## ethnic_groupgroup D:test_prepnone                           1.359 0.174846    
## ethnic_groupgroup E:test_prepnone                           2.308 0.021547 *  
## ethnic_groupgroup B:parent_marital_statusmarried            0.966 0.334542    
## ethnic_groupgroup C:parent_marital_statusmarried            0.206 0.837140    
## ethnic_groupgroup D:parent_marital_statusmarried           -1.372 0.170989    
## ethnic_groupgroup E:parent_marital_statusmarried           -0.115 0.908733    
## ethnic_groupgroup B:parent_marital_statussingle             1.976 0.048918 *  
## ethnic_groupgroup C:parent_marital_statussingle             0.899 0.369157    
## ethnic_groupgroup D:parent_marital_statussingle             0.374 0.708312    
## ethnic_groupgroup E:parent_marital_statussingle             1.513 0.131102    
## ethnic_groupgroup B:parent_marital_statuswidowed            0.481 0.630440    
## ethnic_groupgroup C:parent_marital_statuswidowed            0.925 0.355741    
## ethnic_groupgroup D:parent_marital_statuswidowed            0.054 0.956960    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                 1.388 0.165839    
## ethnic_groupgroup C:practice_sportregularly                 1.402 0.161631    
## ethnic_groupgroup D:practice_sportregularly                 1.040 0.298794    
## ethnic_groupgroup E:practice_sportregularly                 1.453 0.147075    
## ethnic_groupgroup B:practice_sportsometimes                 1.281 0.200908    
## ethnic_groupgroup C:practice_sportsometimes                 2.067 0.039362 *  
## ethnic_groupgroup D:practice_sportsometimes                 1.101 0.271507    
## ethnic_groupgroup E:practice_sportsometimes                 1.348 0.178360    
## ethnic_groupgroup B:is_first_childyes                       1.203 0.229543    
## ethnic_groupgroup C:is_first_childyes                       0.172 0.863639    
## ethnic_groupgroup D:is_first_childyes                      -0.104 0.917334    
## ethnic_groupgroup E:is_first_childyes                       0.001 0.999145    
## ethnic_groupgroup B:transport_meansschool_bus              -1.636 0.102593    
## ethnic_groupgroup C:transport_meansschool_bus              -2.256 0.024637 *  
## ethnic_groupgroup D:transport_meansschool_bus              -0.713 0.476094    
## ethnic_groupgroup E:transport_meansschool_bus              -1.845 0.065857 .  
## ethnic_groupgroup B:wkly_study_hours> 10                   -0.846 0.398354    
## ethnic_groupgroup C:wkly_study_hours> 10                   -0.070 0.944160    
## ethnic_groupgroup D:wkly_study_hours> 10                    0.027 0.978577    
## ethnic_groupgroup E:wkly_study_hours> 10                   -0.259 0.796117    
## ethnic_groupgroup B:wkly_study_hours10-May                 -0.942 0.346753    
## ethnic_groupgroup C:wkly_study_hours10-May                 -0.298 0.765813    
## ethnic_groupgroup D:wkly_study_hours10-May                 -0.283 0.777517    
## ethnic_groupgroup E:wkly_study_hours10-May                 -0.696 0.486909    
## parent_educbachelor's degree:lunch_typestandard             0.107 0.914738    
## parent_educhigh school:lunch_typestandard                   0.197 0.843729    
## parent_educmaster's degree:lunch_typestandard               0.896 0.370878    
## parent_educsome college:lunch_typestandard                  0.816 0.415002    
## parent_educsome high school:lunch_typestandard              1.309 0.191356    
## parent_educbachelor's degree:test_prepnone                 -0.628 0.530209    
## parent_educhigh school:test_prepnone                        0.522 0.601931    
## parent_educmaster's degree:test_prepnone                    0.065 0.948334    
## parent_educsome college:test_prepnone                      -0.745 0.456580    
## parent_educsome high school:test_prepnone                   0.652 0.514864    
## parent_educbachelor's degree:parent_marital_statusmarried  -2.210 0.027665 *  
## parent_educhigh school:parent_marital_statusmarried         0.688 0.491762    
## parent_educmaster's degree:parent_marital_statusmarried     0.090 0.928128    
## parent_educsome college:parent_marital_statusmarried       -1.284 0.200068    
## parent_educsome high school:parent_marital_statusmarried   -0.756 0.449872    
## parent_educbachelor's degree:parent_marital_statussingle   -1.883 0.060511 .  
## parent_educhigh school:parent_marital_statussingle          1.358 0.175196    
## parent_educmaster's degree:parent_marital_statussingle      0.001 0.998882    
## parent_educsome college:parent_marital_statussingle        -0.899 0.369139    
## parent_educsome high school:parent_marital_statussingle    -0.164 0.869653    
## parent_educbachelor's degree:parent_marital_statuswidowed  -0.248 0.804406    
## parent_educhigh school:parent_marital_statuswidowed        -0.598 0.550415    
## parent_educmaster's degree:parent_marital_statuswidowed    -1.534 0.125904    
## parent_educsome college:parent_marital_statuswidowed       -0.949 0.343011    
## parent_educsome high school:parent_marital_statuswidowed   -0.490 0.624733    
## parent_educbachelor's degree:practice_sportregularly       -0.430 0.667700    
## parent_educhigh school:practice_sportregularly             -2.005 0.045673 *  
## parent_educmaster's degree:practice_sportregularly          0.133 0.894397    
## parent_educsome college:practice_sportregularly            -0.051 0.959122    
## parent_educsome high school:practice_sportregularly        -0.550 0.582541    
## parent_educbachelor's degree:practice_sportsometimes       -1.539 0.124621    
## parent_educhigh school:practice_sportsometimes             -1.717 0.086818 .  
## parent_educmaster's degree:practice_sportsometimes          0.756 0.450258    
## parent_educsome college:practice_sportsometimes             0.145 0.884846    
## parent_educsome high school:practice_sportsometimes         0.222 0.824708    
## parent_educbachelor's degree:is_first_childyes              0.946 0.344850    
## parent_educhigh school:is_first_childyes                    1.512 0.131459    
## parent_educmaster's degree:is_first_childyes                0.822 0.411676    
## parent_educsome college:is_first_childyes                   2.262 0.024229 *  
## parent_educsome high school:is_first_childyes               1.128 0.260191    
## parent_educbachelor's degree:transport_meansschool_bus      0.179 0.857717    
## parent_educhigh school:transport_meansschool_bus            0.840 0.401533    
## parent_educmaster's degree:transport_meansschool_bus        0.774 0.439287    
## parent_educsome college:transport_meansschool_bus           0.889 0.374321    
## parent_educsome high school:transport_meansschool_bus       1.443 0.149883    
## parent_educbachelor's degree:wkly_study_hours> 10          -1.099 0.272654    
## parent_educhigh school:wkly_study_hours> 10                -1.344 0.179724    
## parent_educmaster's degree:wkly_study_hours> 10            -0.133 0.894038    
## parent_educsome college:wkly_study_hours> 10               -0.960 0.337663    
## parent_educsome high school:wkly_study_hours> 10           -1.060 0.289895    
## parent_educbachelor's degree:wkly_study_hours10-May        -0.376 0.707482    
## parent_educhigh school:wkly_study_hours10-May              -2.212 0.027535 *  
## parent_educmaster's degree:wkly_study_hours10-May          -0.163 0.870761    
## parent_educsome college:wkly_study_hours10-May             -0.593 0.553816    
## parent_educsome high school:wkly_study_hours10-May         -1.671 0.095514 .  
## lunch_typestandard:test_prepnone                           -1.109 0.268237    
## lunch_typestandard:parent_marital_statusmarried            -1.990 0.047312 *  
## lunch_typestandard:parent_marital_statussingle             -0.806 0.420618    
## lunch_typestandard:parent_marital_statuswidowed             0.119 0.905148    
## lunch_typestandard:practice_sportregularly                  1.335 0.182661    
## lunch_typestandard:practice_sportsometimes                  2.038 0.042245 *  
## lunch_typestandard:is_first_childyes                       -1.204 0.229445    
## lunch_typestandard:transport_meansschool_bus               -1.310 0.191089    
## lunch_typestandard:wkly_study_hours> 10                     1.837 0.066989 .  
## lunch_typestandard:wkly_study_hours10-May                  -0.192 0.848226    
## test_prepnone:parent_marital_statusmarried                  0.932 0.351667    
## test_prepnone:parent_marital_statussingle                  -0.058 0.953813    
## test_prepnone:parent_marital_statuswidowed                 -0.820 0.412702    
## test_prepnone:practice_sportregularly                       0.589 0.556054    
## test_prepnone:practice_sportsometimes                       0.935 0.350295    
## test_prepnone:is_first_childyes                             0.389 0.697562    
## test_prepnone:transport_meansschool_bus                     0.649 0.516419    
## test_prepnone:wkly_study_hours> 10                         -0.639 0.523517    
## test_prepnone:wkly_study_hours10-May                        0.452 0.651763    
## parent_marital_statusmarried:practice_sportregularly        0.507 0.612191    
## parent_marital_statussingle:practice_sportregularly        -0.521 0.602548    
## parent_marital_statuswidowed:practice_sportregularly       -0.083 0.933822    
## parent_marital_statusmarried:practice_sportsometimes        0.202 0.840388    
## parent_marital_statussingle:practice_sportsometimes        -0.522 0.601793    
## parent_marital_statuswidowed:practice_sportsometimes           NA       NA    
## parent_marital_statusmarried:is_first_childyes             -3.591 0.000373 ***
## parent_marital_statussingle:is_first_childyes              -1.613 0.107478    
## parent_marital_statuswidowed:is_first_childyes              0.744 0.457312    
## parent_marital_statusmarried:transport_meansschool_bus      1.108 0.268571    
## parent_marital_statussingle:transport_meansschool_bus      -0.241 0.809421    
## parent_marital_statuswidowed:transport_meansschool_bus     -0.746 0.455903    
## parent_marital_statusmarried:wkly_study_hours> 10           3.431 0.000666 ***
## parent_marital_statussingle:wkly_study_hours> 10            3.956 9.07e-05 ***
## parent_marital_statuswidowed:wkly_study_hours> 10              NA       NA    
## parent_marital_statusmarried:wkly_study_hours10-May         0.804 0.421624    
## parent_marital_statussingle:wkly_study_hours10-May          0.882 0.378225    
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## practice_sportregularly:is_first_childyes                  -0.656 0.512067    
## practice_sportsometimes:is_first_childyes                  -1.092 0.275662    
## practice_sportregularly:transport_meansschool_bus           1.816 0.070179 .  
## practice_sportsometimes:transport_meansschool_bus           1.180 0.238890    
## practice_sportregularly:wkly_study_hours> 10                0.605 0.545817    
## practice_sportsometimes:wkly_study_hours> 10                0.578 0.563797    
## practice_sportregularly:wkly_study_hours10-May              1.459 0.145298    
## practice_sportsometimes:wkly_study_hours10-May              0.071 0.943459    
## is_first_childyes:transport_meansschool_bus                -0.515 0.606629    
## is_first_childyes:wkly_study_hours> 10                      0.492 0.622891    
## is_first_childyes:wkly_study_hours10-May                   -0.873 0.383295    
## transport_meansschool_bus:wkly_study_hours> 10              0.164 0.870166    
## transport_meansschool_bus:wkly_study_hours10-May            0.819 0.413185    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.87 on 383 degrees of freedom
## Multiple R-squared:  0.5303, Adjusted R-squared:  0.2777 
## F-statistic: 2.099 on 206 and 383 DF,  p-value: 2.19e-10
stepwise_model_read <- step(full_fit_read, direction = "both", trace = 1)
## Start:  AIC=3174.13
## reading_score ~ (gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours)^2
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:wkly_study_hours           8     614.8 64084 3163.8
## - parent_educ:wkly_study_hours           10    1420.6 64890 3167.2
## - parent_educ:transport_means             5     415.6 63885 3168.0
## - ethnic_group:parent_educ               20    3769.8 67239 3168.2
## - parent_educ:lunch_type                  5     448.1 63918 3168.3
## - parent_educ:test_prep                   5     452.4 63922 3168.3
## - gender:parent_marital_status            3      36.6 63506 3168.5
## - parent_marital_status:practice_sport    4     295.7 63765 3168.9
## - gender:parent_educ                      5     629.0 64099 3170.0
## - transport_means:wkly_study_hours        2     123.0 63593 3171.3
## - gender:practice_sport                   2     145.0 63615 3171.5
## - test_prep:practice_sport                2     164.3 63634 3171.7
## - ethnic_group:is_first_child             4     609.4 64079 3171.8
## - gender:wkly_study_hours                 2     202.8 63672 3172.0
## - gender:test_prep                        1       1.4 63471 3172.1
## - gender:transport_means                  1       2.9 63473 3172.2
## - test_prep:is_first_child                1      25.1 63495 3172.4
## - gender:lunch_type                       1      25.8 63495 3172.4
## - test_prep:wkly_study_hours              2     242.4 63712 3172.4
## - parent_educ:is_first_child              5     899.0 64369 3172.4
## - is_first_child:transport_means          1      44.0 63514 3172.5
## - practice_sport:is_first_child           2     259.9 63730 3172.5
## - test_prep:transport_means               1      69.9 63539 3172.8
## - is_first_child:wkly_study_hours         2     322.5 63792 3173.1
## - test_prep:parent_marital_status         2     337.8 63807 3173.3
## - parent_educ:parent_marital_status      13    2799.2 66269 3173.6
## - lunch_type:test_prep                    1     203.7 63673 3174.0
## <none>                                                63470 3174.1
## - gender:is_first_child                   1     230.7 63700 3174.3
## - lunch_type:is_first_child               1     240.1 63710 3174.4
## - parent_marital_status:transport_means   3     678.8 64148 3174.4
## - ethnic_group:practice_sport             8    1798.4 65268 3174.6
## - gender:ethnic_group                     4     933.4 64403 3174.7
## - lunch_type:transport_means              1     284.2 63754 3174.8
## - ethnic_group:lunch_type                 4     995.4 64465 3175.3
## - practice_sport:transport_means          2     595.4 64065 3175.6
## - ethnic_group:test_prep                  4    1172.3 64642 3176.9
## - lunch_type:practice_sport               2     753.7 64223 3177.1
## - lunch_type:parent_marital_status        2     780.0 64250 3177.3
## - practice_sport:wkly_study_hours         4    1228.1 64698 3177.4
## - parent_educ:practice_sport             10    2564.7 66034 3177.5
## - lunch_type:wkly_study_hours             2     855.7 64325 3178.0
## - ethnic_group:transport_means            4    1492.9 64962 3179.9
## - ethnic_group:parent_marital_status      9    2935.6 66405 3182.8
## - parent_marital_status:wkly_study_hours  4    2936.1 66406 3192.8
## - parent_marital_status:is_first_child    2    2728.2 66198 3195.0
## 
## Step:  AIC=3163.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:wkly_study_hours + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_educ               20    3674.5 67759 3156.7
## - parent_educ:transport_means             5     373.1 64458 3157.2
## - parent_marital_status:practice_sport    4     207.2 64292 3157.7
## - parent_educ:test_prep                   5     437.9 64522 3157.8
## - parent_educ:wkly_study_hours           10    1542.6 65627 3157.9
## - parent_educ:lunch_type                  5     440.6 64525 3157.9
## - gender:parent_marital_status            3      40.5 64125 3158.2
## - gender:parent_educ                      5     657.6 64742 3159.8
## - transport_means:wkly_study_hours        2      68.6 64153 3160.5
## - gender:wkly_study_hours                 2     148.7 64233 3161.2
## - gender:practice_sport                   2     163.3 64248 3161.3
## - ethnic_group:is_first_child             4     606.3 64691 3161.4
## - test_prep:practice_sport                2     177.1 64261 3161.4
## - gender:transport_means                  1       1.5 64086 3161.8
## - parent_educ:parent_marital_status      13    2664.0 66748 3161.9
## - test_prep:is_first_child                1      10.1 64094 3161.9
## - gender:test_prep                        1      11.1 64095 3161.9
## - gender:lunch_type                       1      32.7 64117 3162.1
## - test_prep:wkly_study_hours              2     253.0 64337 3162.1
## - parent_educ:is_first_child              5     914.6 64999 3162.2
## - is_first_child:transport_means          1      51.4 64136 3162.3
## - practice_sport:is_first_child           2     272.2 64357 3162.3
## - test_prep:transport_means               1      62.9 64147 3162.4
## - test_prep:parent_marital_status         2     349.0 64433 3163.0
## - lunch_type:test_prep                    1     162.2 64247 3163.3
## - is_first_child:wkly_study_hours         2     382.1 64467 3163.3
## - gender:is_first_child                   1     171.5 64256 3163.4
## <none>                                                64084 3163.8
## - gender:ethnic_group                     4     876.2 64961 3163.8
## - ethnic_group:practice_sport             8    1783.4 65868 3164.0
## - lunch_type:is_first_child               1     255.0 64339 3164.2
## - lunch_type:transport_means              1     257.3 64342 3164.2
## - parent_marital_status:transport_means   3     747.2 64832 3164.7
## - practice_sport:transport_means          2     575.9 64660 3165.1
## - ethnic_group:lunch_type                 4    1030.9 65115 3165.2
## - parent_educ:practice_sport             10    2521.2 66606 3166.6
## - lunch_type:practice_sport               2     747.6 64832 3166.7
## - lunch_type:parent_marital_status        2     764.2 64849 3166.8
## - ethnic_group:test_prep                  4    1220.5 65305 3167.0
## - practice_sport:wkly_study_hours         4    1277.6 65362 3167.5
## - lunch_type:wkly_study_hours             2     896.1 64981 3168.0
## - ethnic_group:transport_means            4    1568.2 65653 3170.1
## - ethnic_group:parent_marital_status      9    2898.4 66983 3171.9
## + ethnic_group:wkly_study_hours           8     614.8 63470 3174.1
## - parent_marital_status:wkly_study_hours  4    2786.9 66871 3180.9
## - parent_marital_status:is_first_child    2    2661.3 66746 3183.8
## 
## Step:  AIC=3156.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:wkly_study_hours + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:wkly_study_hours           10    1269.9 69029 3147.7
## - parent_educ:test_prep                   5     307.0 68066 3149.4
## - parent_educ:lunch_type                  5     386.5 68145 3150.1
## - parent_educ:transport_means             5     461.7 68221 3150.7
## - parent_marital_status:practice_sport    4     242.6 68001 3150.8
## - gender:parent_marital_status            3     138.7 67898 3151.9
## - ethnic_group:practice_sport             8    1348.4 69107 3152.3
## - gender:parent_educ                      5     701.3 68460 3152.8
## - parent_educ:is_first_child              5     840.6 68600 3154.0
## - transport_means:wkly_study_hours        2     158.4 67917 3154.1
## - test_prep:practice_sport                2     181.0 67940 3154.3
## - gender:wkly_study_hours                 2     187.1 67946 3154.3
## - is_first_child:wkly_study_hours         2     193.0 67952 3154.4
## - practice_sport:is_first_child           2     209.8 67969 3154.5
## - parent_educ:practice_sport             10    2091.0 69850 3154.6
## - test_prep:is_first_child                1       0.0 67759 3154.7
## - gender:lunch_type                       1       1.5 67760 3154.7
## - gender:transport_means                  1       6.0 67765 3154.8
## - gender:test_prep                        1      28.8 67788 3155.0
## - is_first_child:transport_means          1      31.9 67791 3155.0
## - lunch_type:test_prep                    1      39.0 67798 3155.1
## - gender:is_first_child                   1      53.7 67813 3155.2
## - gender:practice_sport                   2     289.5 68048 3155.2
## - parent_marital_status:transport_means   3     527.4 68286 3155.3
## - test_prep:wkly_study_hours              2     299.0 68058 3155.3
## - lunch_type:parent_marital_status        2     301.2 68060 3155.3
## - ethnic_group:is_first_child             4     776.5 68535 3155.4
## - test_prep:transport_means               1      93.8 67853 3155.5
## - test_prep:parent_marital_status         2     332.4 68091 3155.6
## - parent_educ:parent_marital_status      13    2982.5 70741 3156.1
## - gender:ethnic_group                     4     905.4 68664 3156.5
## - practice_sport:transport_means          2     445.2 68204 3156.6
## <none>                                                67759 3156.7
## - lunch_type:is_first_child               1     315.4 68074 3157.5
## - lunch_type:transport_means              1     316.6 68076 3157.5
## - ethnic_group:test_prep                  4    1135.3 68894 3158.5
## - ethnic_group:lunch_type                 4    1174.9 68934 3158.9
## - practice_sport:wkly_study_hours         4    1254.5 69013 3159.5
## - lunch_type:practice_sport               2     898.1 68657 3160.5
## - ethnic_group:transport_means            4    1420.9 69180 3161.0
## - lunch_type:wkly_study_hours             2    1153.6 68912 3162.7
## + ethnic_group:parent_educ               20    3674.5 64084 3163.8
## - ethnic_group:parent_marital_status      9    2958.5 70717 3163.9
## - parent_marital_status:wkly_study_hours  4    2214.9 69974 3167.7
## + ethnic_group:wkly_study_hours           8     519.5 67239 3168.2
## - parent_marital_status:is_first_child    2    2405.1 70164 3173.3
## 
## Step:  AIC=3147.67
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:lunch_type                  5     320.2 69349 3140.4
## - parent_educ:test_prep                   5     383.5 69412 3140.9
## - parent_marital_status:practice_sport    4     281.9 69311 3142.1
## - parent_educ:transport_means             5     536.0 69565 3142.2
## - gender:parent_marital_status            3     108.9 69138 3142.6
## - ethnic_group:practice_sport             8    1371.2 70400 3143.3
## - gender:parent_educ                      5     719.3 69748 3143.8
## - parent_educ:is_first_child              5     751.8 69781 3144.1
## - is_first_child:wkly_study_hours         2     140.8 69170 3144.9
## - transport_means:wkly_study_hours        2     190.3 69219 3145.3
## - practice_sport:is_first_child           2     196.8 69226 3145.4
## - test_prep:practice_sport                2     233.3 69262 3145.7
## - test_prep:is_first_child                1       0.2 69029 3145.7
## - gender:transport_means                  1       0.3 69029 3145.7
## - gender:lunch_type                       1       3.0 69032 3145.7
## - gender:practice_sport                   2     243.8 69273 3145.8
## - lunch_type:test_prep                    1      17.2 69046 3145.8
## - gender:test_prep                        1      29.3 69058 3145.9
## - is_first_child:transport_means          1      45.0 69074 3146.1
## - gender:is_first_child                   1      76.7 69106 3146.3
## - gender:wkly_study_hours                 2     313.2 69342 3146.3
## - parent_marital_status:transport_means   3     553.7 69582 3146.4
## - test_prep:parent_marital_status         2     325.4 69354 3146.4
## - test_prep:transport_means               1      96.8 69126 3146.5
## - lunch_type:parent_marital_status        2     332.8 69362 3146.5
## - practice_sport:transport_means          2     339.7 69369 3146.6
## - ethnic_group:is_first_child             4     835.0 69864 3146.8
## - test_prep:wkly_study_hours              2     400.0 69429 3147.1
## - gender:ethnic_group                     4     886.0 69915 3147.2
## - parent_educ:practice_sport             10    2344.8 71374 3147.4
## <none>                                                69029 3147.7
## - lunch_type:is_first_child               1     244.1 69273 3147.8
## - ethnic_group:lunch_type                 4     956.4 69985 3147.8
## - practice_sport:wkly_study_hours         4    1068.0 70097 3148.7
## - lunch_type:transport_means              1     366.9 69396 3148.8
## - parent_educ:parent_marital_status      13    3281.5 72310 3149.1
## - ethnic_group:test_prep                  4    1108.8 70138 3149.1
## - lunch_type:practice_sport               2     846.3 69875 3150.9
## - ethnic_group:transport_means            4    1324.6 70353 3150.9
## - lunch_type:wkly_study_hours             2    1037.5 70066 3152.5
## - ethnic_group:parent_marital_status      9    3215.7 72244 3156.5
## + parent_educ:wkly_study_hours           10    1269.9 67759 3156.7
## + ethnic_group:parent_educ               20    3401.8 65627 3157.9
## + ethnic_group:wkly_study_hours           8     590.3 68439 3158.6
## - parent_marital_status:wkly_study_hours  4    2375.7 71404 3159.6
## - parent_marital_status:is_first_child    2    2553.3 71582 3165.1
## 
## Step:  AIC=3140.4
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:test_prep                   5     341.0 69690 3133.3
## - parent_marital_status:practice_sport    4     306.4 69655 3135.0
## - parent_educ:transport_means             5     558.5 69908 3135.1
## - ethnic_group:practice_sport             8    1291.4 70640 3135.3
## - gender:parent_marital_status            3     130.7 69480 3135.5
## - gender:parent_educ                      5     692.2 70041 3136.3
## - parent_educ:is_first_child              5     738.5 70088 3136.7
## - is_first_child:wkly_study_hours         2     148.9 69498 3137.7
## - practice_sport:is_first_child           2     212.5 69561 3138.2
## - transport_means:wkly_study_hours        2     223.6 69573 3138.3
## - gender:transport_means                  1       0.1 69349 3138.4
## - test_prep:is_first_child                1       1.4 69350 3138.4
## - gender:practice_sport                   2     240.3 69589 3138.4
## - gender:lunch_type                       1      11.3 69360 3138.5
## - lunch_type:test_prep                    1      17.1 69366 3138.6
## - test_prep:practice_sport                2     258.3 69607 3138.6
## - gender:test_prep                        1      32.6 69382 3138.7
## - is_first_child:transport_means          1      42.2 69391 3138.8
## - gender:wkly_study_hours                 2     292.4 69641 3138.9
## - lunch_type:parent_marital_status        2     322.6 69672 3139.1
## - test_prep:parent_marital_status         2     339.4 69688 3139.3
## - test_prep:transport_means               1     110.2 69459 3139.3
## - gender:is_first_child                   1     123.4 69472 3139.4
## - parent_marital_status:transport_means   3     609.9 69959 3139.6
## - ethnic_group:is_first_child             4     848.6 70198 3139.6
## - gender:ethnic_group                     4     857.9 70207 3139.7
## - test_prep:wkly_study_hours              2     403.6 69753 3139.8
## - practice_sport:transport_means          2     407.8 69757 3139.9
## - lunch_type:is_first_child               1     218.0 69567 3140.3
## <none>                                                69349 3140.4
## - ethnic_group:lunch_type                 4     951.4 70300 3140.4
## - parent_educ:practice_sport             10    2413.6 71763 3140.6
## - lunch_type:transport_means              1     377.6 69727 3141.6
## - practice_sport:wkly_study_hours         4    1124.5 70474 3141.9
## - ethnic_group:test_prep                  4    1131.5 70481 3141.9
## - parent_educ:parent_marital_status      13    3369.7 72719 3142.4
## - lunch_type:practice_sport               2     809.1 70158 3143.2
## - ethnic_group:transport_means            4    1299.6 70649 3143.4
## - lunch_type:wkly_study_hours             2     993.1 70342 3144.8
## + parent_educ:lunch_type                  5     320.2 69029 3147.7
## - ethnic_group:parent_marital_status      9    3147.4 72496 3148.6
## + parent_educ:wkly_study_hours           10    1203.6 68145 3150.1
## + ethnic_group:parent_educ               20    3421.3 65928 3150.6
## + ethnic_group:wkly_study_hours           8     565.0 68784 3151.6
## - parent_marital_status:wkly_study_hours  4    2520.8 71870 3153.5
## - parent_marital_status:is_first_child    2    2752.7 72102 3159.4
## 
## Step:  AIC=3133.3
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:practice_sport    4     317.6 70008 3128.0
## - ethnic_group:practice_sport             8    1274.2 70964 3128.0
## - gender:parent_marital_status            3     123.8 69814 3128.3
## - gender:parent_educ                      5     652.4 70342 3128.8
## - parent_educ:transport_means             5     667.2 70357 3128.9
## - parent_educ:is_first_child              5     796.7 70487 3130.0
## - is_first_child:wkly_study_hours         2     124.6 69815 3130.3
## - practice_sport:is_first_child           2     200.9 69891 3131.0
## - transport_means:wkly_study_hours        2     208.5 69899 3131.1
## - gender:practice_sport                   2     223.7 69914 3131.2
## - test_prep:practice_sport                2     229.3 69919 3131.2
## - test_prep:is_first_child                1       0.3 69690 3131.3
## - gender:transport_means                  1       1.0 69691 3131.3
## - gender:lunch_type                       1       8.7 69699 3131.4
## - lunch_type:test_prep                    1      19.1 69709 3131.5
## - lunch_type:parent_marital_status        2     264.9 69955 3131.5
## - gender:ethnic_group                     4     753.5 70444 3131.6
## - gender:test_prep                        1      55.9 69746 3131.8
## - test_prep:parent_marital_status         2     301.2 69991 3131.8
## - is_first_child:transport_means          1      67.9 69758 3131.9
## - gender:wkly_study_hours                 2     310.5 70001 3131.9
## - test_prep:transport_means               1     100.3 69790 3132.2
## - gender:is_first_child                   1     104.9 69795 3132.2
## - parent_marital_status:transport_means   3     587.6 70278 3132.2
## - ethnic_group:is_first_child             4     907.0 70597 3132.9
## - practice_sport:transport_means          2     436.3 70126 3133.0
## - test_prep:wkly_study_hours              2     443.2 70133 3133.0
## <none>                                                69690 3133.3
## - ethnic_group:test_prep                  4     951.6 70642 3133.3
## - lunch_type:is_first_child               1     248.8 69939 3133.4
## - parent_educ:practice_sport             10    2425.2 72115 3133.5
## - ethnic_group:lunch_type                 4    1002.5 70692 3133.7
## - lunch_type:transport_means              1     375.0 70065 3134.5
## - parent_educ:parent_marital_status      13    3343.7 73034 3134.9
## - practice_sport:wkly_study_hours         4    1153.2 70843 3135.0
## - ethnic_group:transport_means            4    1310.7 71001 3136.3
## - lunch_type:practice_sport               2     917.5 70608 3137.0
## - lunch_type:wkly_study_hours             2    1061.6 70752 3138.2
## + parent_educ:test_prep                   5     341.0 69349 3140.4
## - ethnic_group:parent_marital_status      9    3065.0 72755 3140.7
## + parent_educ:lunch_type                  5     277.8 69412 3140.9
## + parent_educ:wkly_study_hours           10    1255.7 68434 3142.6
## + ethnic_group:wkly_study_hours           8     565.8 69124 3144.5
## + ethnic_group:parent_educ               20    3212.4 66478 3145.4
## - parent_marital_status:wkly_study_hours  4    2684.2 72374 3147.6
## - parent_marital_status:is_first_child    2    2781.2 72471 3152.4
## 
## Step:  AIC=3127.98
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_marital_status            3     122.7 70130 3123.0
## - ethnic_group:practice_sport             8    1365.0 71373 3123.4
## - gender:parent_educ                      5     663.1 70671 3123.5
## - parent_educ:transport_means             5     690.2 70698 3123.8
## - lunch_type:parent_marital_status        3     322.0 70330 3124.7
## - parent_educ:is_first_child              5     800.9 70809 3124.7
## - practice_sport:is_first_child           2     150.9 70159 3125.2
## - is_first_child:wkly_study_hours         2     163.9 70172 3125.4
## - transport_means:wkly_study_hours        2     204.8 70212 3125.7
## - test_prep:practice_sport                2     236.5 70244 3126.0
## - gender:ethnic_group                     4     714.8 70722 3126.0
## - test_prep:is_first_child                1       0.6 70008 3126.0
## - gender:transport_means                  1       1.9 70010 3126.0
## - gender:lunch_type                       1       7.2 70015 3126.0
## - lunch_type:test_prep                    1      18.2 70026 3126.1
## - gender:practice_sport                   2     264.3 70272 3126.2
## - test_prep:parent_marital_status         2     280.5 70288 3126.3
## - gender:test_prep                        1      66.7 70074 3126.5
## - is_first_child:transport_means          1      87.2 70095 3126.7
## - test_prep:transport_means               1      93.7 70101 3126.8
## - gender:is_first_child                   1      97.3 70105 3126.8
## - gender:wkly_study_hours                 2     342.9 70351 3126.9
## - parent_marital_status:transport_means   3     583.7 70591 3126.9
## - practice_sport:transport_means          2     401.2 70409 3127.3
## - lunch_type:is_first_child               1     177.5 70185 3127.5
## - ethnic_group:is_first_child             4     929.5 70937 3127.8
## - ethnic_group:test_prep                  4     940.7 70948 3127.9
## - test_prep:wkly_study_hours              2     463.2 70471 3127.9
## <none>                                                70008 3128.0
## - parent_educ:practice_sport             10    2449.6 72457 3128.3
## - lunch_type:transport_means              1     337.8 70345 3128.8
## - parent_educ:parent_marital_status      14    3565.4 73573 3129.3
## - ethnic_group:lunch_type                 4    1115.6 71123 3129.3
## - practice_sport:wkly_study_hours         4    1150.0 71158 3129.6
## - ethnic_group:transport_means            4    1283.9 71292 3130.7
## - lunch_type:practice_sport               2     877.2 70885 3131.3
## - lunch_type:wkly_study_hours             2    1099.1 71107 3133.2
## + parent_marital_status:practice_sport    4     317.6 69690 3133.3
## - ethnic_group:parent_marital_status     10    3190.9 73199 3134.3
## + parent_educ:test_prep                   5     352.3 69655 3135.0
## + parent_educ:lunch_type                  5     297.6 69710 3135.5
## + parent_educ:wkly_study_hours           10    1290.0 68718 3137.0
## + ethnic_group:wkly_study_hours           8     481.0 69527 3139.9
## + ethnic_group:parent_educ               20    3249.9 66758 3139.9
## - parent_marital_status:wkly_study_hours  5    2853.2 72861 3141.6
## - parent_marital_status:is_first_child    2    3039.8 73048 3149.1
## 
## Step:  AIC=3123.01
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:practice_sport             8    1356.7 71487 3118.3
## - gender:parent_educ                      5     677.1 70808 3118.7
## - parent_educ:transport_means             5     685.0 70815 3118.8
## - parent_educ:is_first_child              5     819.9 70950 3119.9
## - lunch_type:parent_marital_status        3     369.0 70499 3120.1
## - practice_sport:is_first_child           2     144.7 70275 3120.2
## - is_first_child:wkly_study_hours         2     152.6 70283 3120.3
## - transport_means:wkly_study_hours        2     204.9 70335 3120.7
## - gender:ethnic_group                     4     700.0 70830 3120.9
## - test_prep:is_first_child                1       0.5 70131 3121.0
## - gender:transport_means                  1       1.0 70131 3121.0
## - gender:lunch_type                       1       4.8 70135 3121.1
## - lunch_type:test_prep                    1      21.6 70152 3121.2
## - test_prep:practice_sport                2     266.1 70396 3121.2
## - gender:practice_sport                   2     277.7 70408 3121.3
## - test_prep:parent_marital_status         2     280.8 70411 3121.4
## - gender:test_prep                        1      80.0 70210 3121.7
## - test_prep:transport_means               1      91.3 70222 3121.8
## - is_first_child:transport_means          1     113.9 70244 3122.0
## - gender:is_first_child                   1     114.3 70245 3122.0
## - gender:wkly_study_hours                 2     363.0 70493 3122.1
## - practice_sport:transport_means          2     389.5 70520 3122.3
## - parent_marital_status:transport_means   3     660.2 70791 3122.5
## - lunch_type:is_first_child               1     183.4 70314 3122.6
## - ethnic_group:is_first_child             4     913.5 71044 3122.7
## - test_prep:wkly_study_hours              2     455.4 70586 3122.8
## - ethnic_group:test_prep                  4     952.9 71083 3123.0
## <none>                                                70130 3123.0
## - parent_educ:parent_marital_status      14    3455.4 73586 3123.4
## - lunch_type:transport_means              1     356.3 70487 3124.0
## - ethnic_group:lunch_type                 4    1108.7 71239 3124.3
## - parent_educ:practice_sport             10    2585.2 72716 3124.4
## - practice_sport:wkly_study_hours         4    1194.7 71325 3125.0
## - ethnic_group:transport_means            4    1264.1 71395 3125.6
## - lunch_type:practice_sport               2     959.8 71090 3127.0
## + gender:parent_marital_status            3     122.7 70008 3128.0
## - lunch_type:wkly_study_hours             2    1110.6 71241 3128.3
## + parent_marital_status:practice_sport    4     316.5 69814 3128.3
## - ethnic_group:parent_marital_status     10    3250.3 73381 3129.7
## + parent_educ:test_prep                   5     345.4 69785 3130.1
## + parent_educ:lunch_type                  5     315.8 69815 3130.3
## + parent_educ:wkly_study_hours           10    1252.2 68878 3132.4
## + ethnic_group:parent_educ               20    3339.0 66791 3134.2
## + ethnic_group:wkly_study_hours           8     511.2 69619 3134.7
## - parent_marital_status:wkly_study_hours  5    2844.3 72975 3136.5
## - parent_marital_status:is_first_child    2    3138.1 73269 3144.8
## 
## Step:  AIC=3118.32
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:transport_means             5     548.5 72036 3112.8
## - gender:parent_educ                      5     581.6 72069 3113.1
## - gender:ethnic_group                     4     534.8 72022 3114.7
## - practice_sport:is_first_child           2     121.8 71609 3115.3
## - lunch_type:parent_marital_status        3     394.4 71882 3115.6
## - is_first_child:wkly_study_hours         2     177.5 71665 3115.8
## - test_prep:practice_sport                2     196.3 71683 3115.9
## - parent_educ:is_first_child              5     939.4 72427 3116.0
## - transport_means:wkly_study_hours        2     221.2 71708 3116.1
## - lunch_type:test_prep                    1       0.0 71487 3116.3
## - gender:lunch_type                       1       0.1 71487 3116.3
## - gender:transport_means                  1       0.3 71487 3116.3
## - test_prep:is_first_child                1       0.7 71488 3116.3
## - gender:test_prep                        1      50.9 71538 3116.7
## - gender:is_first_child                   1      53.6 71541 3116.8
## - test_prep:parent_marital_status         2     313.1 71800 3116.9
## - ethnic_group:is_first_child             4     825.4 72313 3117.1
## - test_prep:wkly_study_hours              2     338.3 71825 3117.1
## - test_prep:transport_means               1     106.9 71594 3117.2
## - practice_sport:transport_means          2     376.1 71863 3117.4
## - is_first_child:transport_means          1     164.3 71651 3117.7
## - ethnic_group:test_prep                  4     919.2 72406 3117.9
## - gender:practice_sport                   2     453.1 71940 3118.1
## <none>                                                71487 3118.3
## - gender:wkly_study_hours                 2     487.4 71974 3118.3
## - lunch_type:is_first_child               1     245.8 71733 3118.3
## - lunch_type:transport_means              1     258.5 71746 3118.4
## - parent_educ:parent_marital_status      14    3522.4 75010 3118.7
## - parent_marital_status:transport_means   3     781.1 72268 3118.7
## - parent_educ:practice_sport             10    2650.7 74138 3119.8
## - practice_sport:wkly_study_hours         4    1180.8 72668 3120.0
## - ethnic_group:lunch_type                 4    1274.7 72762 3120.8
## - ethnic_group:transport_means            4    1324.6 72812 3121.2
## - lunch_type:practice_sport               2     969.1 72456 3122.3
## + parent_marital_status:practice_sport    4     402.2 71085 3123.0
## + ethnic_group:practice_sport             8    1356.7 70130 3123.0
## - lunch_type:wkly_study_hours             2    1089.7 72577 3123.2
## + gender:parent_marital_status            3     114.4 71373 3123.4
## - ethnic_group:parent_marital_status     10    3370.4 74858 3125.5
## + parent_educ:test_prep                   5     312.5 71175 3125.7
## + parent_educ:lunch_type                  5     224.8 71262 3126.5
## + parent_educ:wkly_study_hours           10    1304.6 70182 3127.4
## + ethnic_group:wkly_study_hours           8     473.3 71014 3130.4
## - parent_marital_status:wkly_study_hours  5    2938.9 74426 3132.1
## + ethnic_group:parent_educ               20    2867.8 68619 3134.2
## - parent_marital_status:is_first_child    2    2933.5 74421 3138.1
## 
## Step:  AIC=3112.83
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_educ                      5     603.8 72639 3107.8
## - gender:ethnic_group                     4     475.9 72512 3108.7
## - practice_sport:is_first_child           2      88.0 72124 3109.6
## - is_first_child:wkly_study_hours         2     178.3 72214 3110.3
## - test_prep:practice_sport                2     197.3 72233 3110.4
## - lunch_type:parent_marital_status        3     454.7 72490 3110.5
## - parent_educ:is_first_child              5     958.0 72994 3110.6
## - transport_means:wkly_study_hours        2     234.3 72270 3110.7
## - gender:transport_means                  1       0.0 72036 3110.8
## - test_prep:is_first_child                1       0.9 72036 3110.8
## - gender:lunch_type                       1       1.7 72037 3110.8
## - lunch_type:test_prep                    1       2.7 72038 3110.8
## - gender:test_prep                        1      37.7 72073 3111.1
## - test_prep:parent_marital_status         2     287.2 72323 3111.2
## - gender:is_first_child                   1      49.1 72085 3111.2
## - practice_sport:transport_means          2     304.8 72340 3111.3
## - test_prep:wkly_study_hours              2     352.0 72388 3111.7
## - is_first_child:transport_means          1     135.0 72171 3111.9
## - ethnic_group:is_first_child             4     874.0 72910 3111.9
## - test_prep:transport_means               1     146.1 72182 3112.0
## - parent_marital_status:transport_means   3     668.1 72704 3112.3
## - gender:wkly_study_hours                 2     433.5 72469 3112.4
## - parent_educ:parent_marital_status      14    3444.3 75480 3112.4
## - ethnic_group:test_prep                  4     945.8 72981 3112.5
## - gender:practice_sport                   2     458.7 72494 3112.6
## - lunch_type:is_first_child               1     235.4 72271 3112.8
## <none>                                                72036 3112.8
## - lunch_type:transport_means              1     251.0 72287 3112.9
## - parent_educ:practice_sport             10    2633.4 74669 3114.0
## - practice_sport:wkly_study_hours         4    1297.2 73333 3115.4
## - ethnic_group:lunch_type                 4    1387.9 73424 3116.1
## - ethnic_group:transport_means            4    1456.2 73492 3116.6
## - lunch_type:practice_sport               2     986.4 73022 3116.8
## + parent_marital_status:practice_sport    4     414.6 71621 3117.4
## + gender:parent_marital_status            3     109.2 71926 3117.9
## + parent_educ:transport_means             5     548.5 71487 3118.3
## - lunch_type:wkly_study_hours             2    1169.8 73205 3118.3
## + ethnic_group:practice_sport             8    1220.2 70815 3118.8
## + parent_educ:test_prep                   5     395.4 71640 3119.6
## - ethnic_group:parent_marital_status     10    3435.4 75471 3120.3
## + parent_educ:lunch_type                  5     241.7 71794 3120.8
## + parent_educ:wkly_study_hours           10    1335.5 70700 3121.8
## + ethnic_group:wkly_study_hours           8     495.2 71540 3124.8
## - parent_marital_status:wkly_study_hours  5    3004.4 75040 3126.9
## + ethnic_group:parent_educ               20    3017.4 69018 3127.6
## - parent_marital_status:is_first_child    2    2981.2 75017 3132.8
## 
## Step:  AIC=3107.75
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:lunch_type + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:ethnic_group                     4     357.5 72997 3102.7
## - parent_educ:is_first_child              5     838.9 73478 3104.5
## - practice_sport:is_first_child           2     105.8 72745 3104.6
## - lunch_type:parent_marital_status        3     422.0 73061 3105.2
## - is_first_child:wkly_study_hours         2     205.4 72845 3105.4
## - transport_means:wkly_study_hours        2     231.0 72870 3105.6
## - gender:transport_means                  1       0.0 72639 3105.8
## - gender:lunch_type                       1       1.4 72641 3105.8
## - test_prep:is_first_child                1       4.8 72644 3105.8
## - lunch_type:test_prep                    1      11.0 72650 3105.8
## - test_prep:practice_sport                2     260.4 72900 3105.9
## - test_prep:parent_marital_status         2     267.3 72907 3105.9
## - gender:test_prep                        1      27.3 72667 3106.0
## - practice_sport:transport_means          2     287.5 72927 3106.1
## - gender:is_first_child                   1      46.8 72686 3106.1
## - ethnic_group:test_prep                  4     856.3 73496 3106.7
## - ethnic_group:is_first_child             4     858.1 73497 3106.7
## - is_first_child:transport_means          1     127.0 72766 3106.8
## - test_prep:transport_means               1     128.8 72768 3106.8
## - test_prep:wkly_study_hours              2     412.9 73052 3107.1
## - gender:wkly_study_hours                 2     454.8 73094 3107.4
## - gender:practice_sport                   2     463.1 73103 3107.5
## - lunch_type:is_first_child               1     216.9 72856 3107.5
## - parent_marital_status:transport_means   3     724.1 73363 3107.6
## <none>                                                72639 3107.8
## - parent_educ:practice_sport             10    2551.6 75191 3108.1
## - lunch_type:transport_means              1     333.5 72973 3108.5
## - parent_educ:parent_marital_status      14    3774.3 76414 3109.6
## - practice_sport:wkly_study_hours         4    1233.1 73872 3109.7
## - ethnic_group:lunch_type                 4    1289.5 73929 3110.1
## - lunch_type:practice_sport               2     942.3 73582 3111.4
## + parent_marital_status:practice_sport    4     431.9 72207 3112.2
## - ethnic_group:transport_means            4    1600.7 74240 3112.6
## + gender:parent_educ                      5     603.8 72036 3112.8
## + gender:parent_marital_status            3     108.8 72531 3112.9
## - lunch_type:wkly_study_hours             2    1157.9 73797 3113.1
## + parent_educ:transport_means             5     570.6 72069 3113.1
## - ethnic_group:parent_marital_status     10    3305.3 75945 3114.0
## + ethnic_group:practice_sport             8    1130.0 71509 3114.5
## + parent_educ:test_prep                   5     351.2 72288 3114.9
## + parent_educ:lunch_type                  5     235.7 72404 3115.8
## + parent_educ:wkly_study_hours           10    1314.3 71325 3117.0
## + ethnic_group:wkly_study_hours           8     515.2 72124 3119.6
## + ethnic_group:parent_educ               20    3119.5 69520 3121.9
## - parent_marital_status:wkly_study_hours  5    3076.4 75716 3122.2
## - parent_marital_status:is_first_child    2    2985.7 75625 3127.5
## 
## Step:  AIC=3102.65
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:is_first_child           2     121.5 73118 3099.6
## - lunch_type:parent_marital_status        3     402.0 73399 3099.9
## - is_first_child:wkly_study_hours         2     204.6 73201 3100.3
## - parent_educ:is_first_child              5     960.2 73957 3100.4
## - ethnic_group:test_prep                  4     712.7 73710 3100.4
## - transport_means:wkly_study_hours        2     234.6 73231 3100.5
## - gender:lunch_type                       1       0.3 72997 3100.7
## - gender:transport_means                  1       1.6 72998 3100.7
## - test_prep:parent_marital_status         2     250.2 73247 3100.7
## - test_prep:is_first_child                1       5.9 73003 3100.7
## - test_prep:practice_sport                2     258.1 73255 3100.7
## - lunch_type:test_prep                    1      18.8 73016 3100.8
## - gender:test_prep                        1      19.3 73016 3100.8
## - practice_sport:transport_means          2     282.8 73280 3100.9
## - gender:is_first_child                   1      55.7 73052 3101.1
## - ethnic_group:is_first_child             4     838.1 73835 3101.4
## - test_prep:transport_means               1     135.7 73132 3101.7
## - is_first_child:transport_means          1     147.7 73145 3101.8
## - test_prep:wkly_study_hours              2     417.8 73415 3102.0
## - gender:practice_sport                   2     467.7 73465 3102.4
## - lunch_type:is_first_child               1     223.6 73220 3102.4
## <none>                                                72997 3102.7
## - gender:wkly_study_hours                 2     497.9 73495 3102.7
## - parent_marital_status:transport_means   3     785.6 73782 3103.0
## - parent_educ:practice_sport             10    2563.4 75560 3103.0
## - lunch_type:transport_means              1     326.1 73323 3103.3
## - ethnic_group:lunch_type                 4    1273.0 74270 3104.8
## - practice_sport:wkly_study_hours         4    1285.8 74283 3104.9
## - parent_educ:parent_marital_status      14    3916.8 76914 3105.5
## - lunch_type:practice_sport               2    1063.9 74061 3107.2
## + parent_marital_status:practice_sport    4     401.1 72596 3107.4
## - ethnic_group:transport_means            4    1601.0 74598 3107.4
## - ethnic_group:parent_marital_status     10    3170.2 76167 3107.7
## + gender:ethnic_group                     4     357.5 72639 3107.8
## + gender:parent_marital_status            3     100.5 72896 3107.8
## - lunch_type:wkly_study_hours             2    1180.5 74177 3108.1
## + parent_educ:transport_means             5     515.8 72481 3108.5
## + gender:parent_educ                      5     485.3 72512 3108.7
## + ethnic_group:practice_sport             8    1051.0 71946 3110.1
## + parent_educ:test_prep                   5     256.9 72740 3110.6
## + parent_educ:lunch_type                  5     226.0 72771 3110.8
## + parent_educ:wkly_study_hours           10    1282.6 71714 3112.2
## + ethnic_group:wkly_study_hours           8     491.4 72505 3114.7
## - parent_marital_status:wkly_study_hours  5    3086.2 76083 3117.1
## + ethnic_group:parent_educ               20    3022.3 69974 3117.7
## - parent_marital_status:is_first_child    2    3076.4 76073 3123.0
## 
## Step:  AIC=3099.63
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:parent_marital_status        3     374.8 73493 3096.7
## - is_first_child:wkly_study_hours         2     186.9 73305 3097.1
## - parent_educ:is_first_child              5     949.9 74068 3097.2
## - ethnic_group:test_prep                  4     732.4 73851 3097.5
## - transport_means:wkly_study_hours        2     238.0 73356 3097.6
## - test_prep:parent_marital_status         2     246.9 73365 3097.6
## - gender:lunch_type                       1       0.3 73119 3097.6
## - test_prep:is_first_child                1       1.5 73120 3097.6
## - gender:transport_means                  1       2.9 73121 3097.7
## - lunch_type:test_prep                    1      23.0 73141 3097.8
## - practice_sport:transport_means          2     271.5 73390 3097.8
## - gender:test_prep                        1      24.4 73143 3097.8
## - test_prep:practice_sport                2     282.1 73400 3097.9
## - gender:is_first_child                   1      66.2 73184 3098.2
## - ethnic_group:is_first_child             4     870.1 73988 3098.6
## - test_prep:transport_means               1     138.4 73257 3098.8
## - test_prep:wkly_study_hours              2     402.6 73521 3098.9
## - is_first_child:transport_means          1     164.6 73283 3099.0
## - gender:practice_sport                   2     455.9 73574 3099.3
## - gender:wkly_study_hours                 2     489.8 73608 3099.6
## - lunch_type:is_first_child               1     245.7 73364 3099.6
## - parent_marital_status:transport_means   3     746.7 73865 3099.6
## <none>                                                73118 3099.6
## - parent_educ:practice_sport             10    2528.0 75646 3099.7
## - lunch_type:transport_means              1     326.5 73445 3100.3
## - ethnic_group:lunch_type                 4    1294.0 74412 3102.0
## - parent_educ:parent_marital_status      14    3861.6 76980 3102.0
## - practice_sport:wkly_study_hours         4    1302.5 74421 3102.1
## + practice_sport:is_first_child           2     121.5 72997 3102.7
## - ethnic_group:transport_means            4    1550.5 74669 3104.0
## - lunch_type:practice_sport               2    1065.3 74184 3104.2
## - ethnic_group:parent_marital_status     10    3109.3 76228 3104.2
## + gender:ethnic_group                     4     373.1 72745 3104.6
## + parent_marital_status:practice_sport    4     367.7 72751 3104.7
## + gender:parent_marital_status            3      88.8 73030 3104.9
## - lunch_type:wkly_study_hours             2    1188.6 74307 3105.1
## + gender:parent_educ                      5     501.0 72617 3105.6
## + parent_educ:transport_means             5     474.9 72643 3105.8
## + ethnic_group:practice_sport             8    1036.1 72082 3107.2
## + parent_educ:test_prep                   5     245.0 72873 3107.7
## + parent_educ:lunch_type                  5     228.7 72890 3107.8
## + parent_educ:wkly_study_hours           10    1277.4 71841 3109.2
## + ethnic_group:wkly_study_hours           8     505.9 72612 3111.5
## - parent_marital_status:wkly_study_hours  5    3089.3 76208 3114.1
## + ethnic_group:parent_educ               20    2920.9 70197 3115.6
## - parent_marital_status:is_first_child    2    3028.3 76147 3119.6
## 
## Step:  AIC=3096.65
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:is_first_child              5     908.9 74402 3093.9
## - is_first_child:wkly_study_hours         2     173.4 73667 3094.0
## - test_prep:parent_marital_status         2     234.7 73728 3094.5
## - test_prep:is_first_child                1       1.1 73494 3094.7
## - ethnic_group:test_prep                  4     753.5 74247 3094.7
## - gender:lunch_type                       1       6.4 73500 3094.7
## - gender:transport_means                  1       6.7 73500 3094.7
## - lunch_type:test_prep                    1      20.6 73514 3094.8
## - practice_sport:transport_means          2     273.6 73767 3094.8
## - transport_means:wkly_study_hours        2     274.4 73767 3094.8
## - gender:test_prep                        1      35.5 73529 3094.9
## - test_prep:practice_sport                2     290.9 73784 3095.0
## - ethnic_group:is_first_child             4     829.3 74322 3095.3
## - gender:is_first_child                   1      81.0 73574 3095.3
## - test_prep:transport_means               1     136.1 73629 3095.7
## - test_prep:wkly_study_hours              2     402.3 73895 3095.9
## - gender:practice_sport                   2     412.2 73905 3095.9
## - is_first_child:transport_means          1     175.2 73668 3096.1
## - gender:wkly_study_hours                 2     431.3 73924 3096.1
## - lunch_type:is_first_child               1     218.5 73712 3096.4
## - parent_marital_status:transport_means   3     743.8 74237 3096.6
## <none>                                                73493 3096.7
## - parent_educ:practice_sport             10    2548.8 76042 3096.8
## - lunch_type:transport_means              1     328.3 73821 3097.3
## - practice_sport:wkly_study_hours         4    1295.6 74789 3099.0
## - parent_educ:parent_marital_status      14    3920.7 77414 3099.3
## + lunch_type:parent_marital_status        3     374.8 73118 3099.6
## - ethnic_group:lunch_type                 4    1393.2 74886 3099.7
## + practice_sport:is_first_child           2      94.3 73399 3099.9
## - lunch_type:practice_sport               2     998.0 74491 3100.6
## - ethnic_group:parent_marital_status     10    3049.2 76542 3100.6
## - ethnic_group:transport_means            4    1542.9 75036 3100.9
## - lunch_type:wkly_study_hours             2    1093.4 74587 3101.4
## + gender:parent_marital_status            3     124.4 73369 3101.7
## + gender:ethnic_group                     4     351.9 73141 3101.8
## + parent_educ:transport_means             5     521.3 72972 3102.4
## + gender:parent_educ                      5     479.0 73014 3102.8
## + parent_marital_status:practice_sport    5     428.2 73065 3103.2
## + ethnic_group:practice_sport             8    1039.1 72454 3104.2
## + parent_educ:lunch_type                  5     221.6 73272 3104.9
## + parent_educ:test_prep                   5     214.7 73278 3104.9
## + parent_educ:wkly_study_hours           10    1282.2 72211 3106.3
## + ethnic_group:wkly_study_hours           8     478.5 73015 3108.8
## - parent_marital_status:wkly_study_hours  5    2984.5 76478 3110.1
## + ethnic_group:parent_educ               20    2625.3 70868 3115.2
## - parent_marital_status:is_first_child    2    3010.8 76504 3116.3
## 
## Step:  AIC=3093.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - is_first_child:wkly_study_hours         2     116.1 74518 3090.8
## - test_prep:parent_marital_status         2     216.2 74618 3091.6
## - test_prep:is_first_child                1       1.0 74403 3091.9
## - gender:transport_means                  1       2.7 74405 3091.9
## - gender:lunch_type                       1       4.7 74407 3091.9
## - transport_means:wkly_study_hours        2     263.8 74666 3092.0
## - ethnic_group:test_prep                  4     772.1 75174 3092.0
## - lunch_type:test_prep                    1      14.6 74417 3092.0
## - practice_sport:transport_means          2     278.7 74681 3092.1
## - gender:test_prep                        1      36.6 74439 3092.2
## - ethnic_group:is_first_child             4     820.4 75222 3092.4
## - parent_marital_status:transport_means   3     608.0 75010 3092.7
## - gender:is_first_child                   1     113.6 74516 3092.8
## - test_prep:transport_means               1     159.0 74561 3093.2
## - test_prep:practice_sport                2     417.4 74819 3093.2
## - gender:wkly_study_hours                 2     418.8 74821 3093.2
## - test_prep:wkly_study_hours              2     435.0 74837 3093.3
## - is_first_child:transport_means          1     223.9 74626 3093.7
## - gender:practice_sport                   2     478.2 74880 3093.7
## - lunch_type:is_first_child               1     250.2 74652 3093.9
## <none>                                                74402 3093.9
## - lunch_type:transport_means              1     305.0 74707 3094.3
## - parent_educ:practice_sport             10    2677.4 77079 3094.8
## - practice_sport:wkly_study_hours         4    1145.4 75547 3094.9
## - parent_educ:parent_marital_status      14    3963.2 78365 3096.5
## + parent_educ:is_first_child              5     908.9 73493 3096.7
## - ethnic_group:lunch_type                 4    1401.7 75804 3096.9
## - ethnic_group:parent_marital_status     10    2988.4 77390 3097.1
## + practice_sport:is_first_child           2      89.6 74312 3097.2
## + lunch_type:parent_marital_status        3     333.8 74068 3097.2
## - lunch_type:wkly_study_hours             2     987.7 75390 3097.7
## - lunch_type:practice_sport               2    1005.9 75408 3097.8
## + gender:ethnic_group                     4     468.2 73934 3098.2
## - ethnic_group:transport_means            4    1592.6 75995 3098.4
## + gender:parent_marital_status            3     140.4 74262 3098.8
## + parent_educ:transport_means             5     540.0 73862 3099.6
## + parent_marital_status:practice_sport    5     445.6 73956 3100.3
## + gender:parent_educ                      5     357.5 74045 3101.1
## + ethnic_group:practice_sport             8    1093.6 73308 3101.2
## + parent_educ:test_prep                   5     283.3 74119 3101.7
## + parent_educ:lunch_type                  5     216.9 74185 3102.2
## + parent_educ:wkly_study_hours           10    1215.8 73186 3104.2
## + ethnic_group:wkly_study_hours           8     490.9 73911 3106.0
## - parent_marital_status:wkly_study_hours  5    2913.7 77316 3106.6
## - parent_marital_status:is_first_child    2    2779.0 77181 3111.5
## + ethnic_group:parent_educ               20    2651.5 71751 3112.5
## 
## Step:  AIC=3090.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:parent_marital_status         2     226.9 74745 3088.6
## - ethnic_group:test_prep                  4     755.2 75273 3088.8
## - test_prep:is_first_child                1       3.6 74522 3088.8
## - gender:lunch_type                       1       4.0 74522 3088.8
## - gender:transport_means                  1       5.2 74523 3088.9
## - lunch_type:test_prep                    1      20.2 74538 3089.0
## - transport_means:wkly_study_hours        2     276.9 74795 3089.0
## - practice_sport:transport_means          2     283.8 74802 3089.1
## - gender:test_prep                        1      39.9 74558 3089.1
## - parent_marital_status:transport_means   3     560.5 75079 3089.2
## - gender:is_first_child                   1     131.9 74650 3089.9
## - test_prep:practice_sport                2     389.2 74907 3089.9
## - ethnic_group:is_first_child             4     902.5 75421 3089.9
## - gender:wkly_study_hours                 2     420.9 74939 3090.1
## - test_prep:transport_means               1     178.7 74697 3090.2
## - test_prep:wkly_study_hours              2     447.6 74966 3090.3
## - is_first_child:transport_means          1     207.2 74725 3090.5
## - gender:practice_sport                   2     487.0 75005 3090.7
## <none>                                                74518 3090.8
## - lunch_type:is_first_child               1     281.2 74799 3091.0
## - lunch_type:transport_means              1     316.1 74834 3091.3
## - parent_educ:practice_sport             10    2637.3 77155 3091.3
## - practice_sport:wkly_study_hours         4    1218.6 75737 3092.4
## - ethnic_group:parent_marital_status     10    2949.1 77467 3093.7
## + is_first_child:wkly_study_hours         2     116.1 74402 3093.9
## - ethnic_group:lunch_type                 4    1419.2 75937 3093.9
## + parent_educ:is_first_child              5     851.5 73667 3094.0
## + practice_sport:is_first_child           2      79.9 74438 3094.2
## - parent_educ:parent_marital_status      14    4073.8 78592 3094.2
## + lunch_type:parent_marital_status        3     325.4 74193 3094.2
## - lunch_type:wkly_study_hours             2    1008.5 75527 3094.8
## - ethnic_group:transport_means            4    1571.5 76090 3095.1
## + gender:ethnic_group                     4     463.4 74055 3095.1
## - lunch_type:practice_sport               2    1106.6 75625 3095.5
## + gender:parent_marital_status            3     122.9 74395 3095.8
## + parent_educ:transport_means             5     533.4 73985 3096.6
## + parent_marital_status:practice_sport    5     480.3 74038 3097.0
## + gender:parent_educ                      5     382.2 74136 3097.8
## + ethnic_group:practice_sport             8    1106.0 73412 3098.0
## + parent_educ:test_prep                   5     252.5 74266 3098.8
## + parent_educ:lunch_type                  5     226.9 74291 3099.0
## + parent_educ:wkly_study_hours           10    1196.3 73322 3101.3
## + ethnic_group:wkly_study_hours           8     531.7 73986 3102.6
## - parent_marital_status:wkly_study_hours  5    2935.4 77454 3103.6
## - parent_marital_status:is_first_child    2    2749.1 77267 3108.2
## + ethnic_group:parent_educ               20    2507.0 72011 3110.6
## 
## Step:  AIC=3088.61
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:is_first_child                1       0.0 74745 3086.6
## - gender:transport_means                  1       3.1 74748 3086.6
## - gender:lunch_type                       1       3.2 74748 3086.6
## - ethnic_group:test_prep                  4     771.7 75517 3086.7
## - lunch_type:test_prep                    1      19.0 74764 3086.8
## - transport_means:wkly_study_hours        2     274.1 75019 3086.8
## - practice_sport:transport_means          2     282.2 75027 3086.8
## - gender:test_prep                        1      33.7 74779 3086.9
## - parent_marital_status:transport_means   3     637.6 75383 3087.6
## - gender:is_first_child                   1     140.0 74885 3087.7
## - gender:wkly_study_hours                 2     427.7 75173 3088.0
## - test_prep:practice_sport                2     430.9 75176 3088.0
## - test_prep:wkly_study_hours              2     443.8 75189 3088.1
## - is_first_child:transport_means          1     194.2 74939 3088.1
## - test_prep:transport_means               1     204.7 74950 3088.2
## - gender:practice_sport                   2     473.1 75218 3088.3
## - ethnic_group:is_first_child             4     989.3 75734 3088.4
## <none>                                                74745 3088.6
## - lunch_type:is_first_child               1     262.7 75008 3088.7
## - parent_educ:practice_sport             10    2614.3 77359 3088.9
## - lunch_type:transport_means              1     313.3 75058 3089.1
## - ethnic_group:parent_marital_status     11    2935.6 77681 3089.3
## - parent_educ:parent_marital_status      15    4085.3 78830 3090.0
## - practice_sport:wkly_study_hours         4    1210.8 75956 3090.1
## + test_prep:parent_marital_status         2     226.9 74518 3090.8
## + is_first_child:wkly_study_hours         2     126.8 74618 3091.6
## + parent_educ:is_first_child              5     831.9 73913 3092.0
## + practice_sport:is_first_child           2      75.7 74669 3092.0
## - ethnic_group:lunch_type                 4    1478.6 76224 3092.2
## + lunch_type:parent_marital_status        3     308.8 74436 3092.2
## - lunch_type:wkly_study_hours             2    1020.1 75765 3092.6
## - lunch_type:practice_sport               2    1054.2 75799 3092.9
## + gender:ethnic_group                     4     446.6 74298 3093.1
## - ethnic_group:transport_means            4    1611.0 76356 3093.2
## + gender:parent_marital_status            3     127.1 74618 3093.6
## + parent_educ:transport_means             5     508.2 74237 3094.6
## + parent_marital_status:practice_sport    5     478.0 74267 3094.8
## + ethnic_group:practice_sport             8    1145.2 73600 3095.5
## + gender:parent_educ                      5     370.5 74374 3095.7
## + parent_educ:lunch_type                  5     254.2 74491 3096.6
## + parent_educ:test_prep                   5     216.4 74529 3096.9
## + parent_educ:wkly_study_hours           10    1231.3 73514 3098.8
## + ethnic_group:wkly_study_hours           8     555.6 74189 3100.2
## - parent_marital_status:wkly_study_hours  6    3151.7 77897 3101.0
## - parent_marital_status:is_first_child    3    2970.8 77716 3105.6
## + ethnic_group:parent_educ               20    2580.0 72165 3107.9
## 
## Step:  AIC=3086.61
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:transport_means                  1       3.1 74748 3084.6
## - gender:lunch_type                       1       3.2 74748 3084.6
## - ethnic_group:test_prep                  4     773.4 75518 3084.7
## - lunch_type:test_prep                    1      19.0 74764 3084.8
## - transport_means:wkly_study_hours        2     274.3 75019 3084.8
## - practice_sport:transport_means          2     282.1 75027 3084.8
## - gender:test_prep                        1      33.7 74779 3084.9
## - parent_marital_status:transport_means   3     638.4 75383 3085.6
## - gender:is_first_child                   1     140.6 74886 3085.7
## - gender:wkly_study_hours                 2     429.3 75174 3086.0
## - test_prep:practice_sport                2     431.0 75176 3086.0
## - test_prep:wkly_study_hours              2     443.8 75189 3086.1
## - is_first_child:transport_means          1     194.3 74939 3086.1
## - test_prep:transport_means               1     204.7 74950 3086.2
## - gender:practice_sport                   2     474.3 75219 3086.3
## - ethnic_group:is_first_child             4     990.3 75735 3086.4
## <none>                                                74745 3086.6
## - lunch_type:is_first_child               1     263.8 75009 3086.7
## - parent_educ:practice_sport             10    2614.7 77360 3086.9
## - lunch_type:transport_means              1     315.2 75060 3087.1
## - ethnic_group:parent_marital_status     11    2937.1 77682 3087.3
## - parent_educ:parent_marital_status      15    4085.4 78830 3088.0
## - practice_sport:wkly_study_hours         4    1213.1 75958 3088.1
## + test_prep:is_first_child                1       0.0 74745 3088.6
## + test_prep:parent_marital_status         2     223.3 74522 3088.8
## + is_first_child:wkly_study_hours         2     126.2 74619 3089.6
## + practice_sport:is_first_child           2      75.4 74670 3090.0
## + parent_educ:is_first_child              5     828.7 73916 3090.0
## + lunch_type:parent_marital_status        3     308.7 74436 3090.2
## - ethnic_group:lunch_type                 4    1481.4 76226 3090.2
## - lunch_type:wkly_study_hours             2    1020.8 75766 3090.6
## - lunch_type:practice_sport               2    1055.5 75800 3090.9
## + gender:ethnic_group                     4     446.6 74298 3091.1
## - ethnic_group:transport_means            4    1611.0 76356 3091.2
## + gender:parent_marital_status            3     126.9 74618 3091.6
## + parent_educ:transport_means             5     504.6 74240 3092.6
## + parent_marital_status:practice_sport    5     478.0 74267 3092.8
## + ethnic_group:practice_sport             8    1145.0 73600 3093.5
## + gender:parent_educ                      5     369.4 74376 3093.7
## + parent_educ:lunch_type                  5     254.2 74491 3094.6
## + parent_educ:test_prep                   5     216.1 74529 3094.9
## + parent_educ:wkly_study_hours           10    1230.4 73515 3096.8
## + ethnic_group:wkly_study_hours           8     552.7 74192 3098.2
## - parent_marital_status:wkly_study_hours  6    3152.6 77898 3099.0
## - parent_marital_status:is_first_child    3    2971.0 77716 3103.6
## + ethnic_group:parent_educ               20    2568.1 72177 3106.0
## 
## Step:  AIC=3084.64
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:lunch_type                       1       3.4 74751 3082.7
## - ethnic_group:test_prep                  4     772.2 75520 3082.7
## - lunch_type:test_prep                    1      19.4 74767 3082.8
## - transport_means:wkly_study_hours        2     274.4 75022 3082.8
## - practice_sport:transport_means          2     282.4 75030 3082.9
## - gender:test_prep                        1      32.1 74780 3082.9
## - parent_marital_status:transport_means   3     637.5 75386 3083.7
## - gender:is_first_child                   1     140.3 74888 3083.7
## - test_prep:practice_sport                2     430.3 75178 3084.0
## - gender:wkly_study_hours                 2     430.5 75179 3084.0
## - test_prep:wkly_study_hours              2     443.4 75191 3084.1
## - is_first_child:transport_means          1     197.9 74946 3084.2
## - test_prep:transport_means               1     209.1 74957 3084.3
## - gender:practice_sport                   2     476.3 75224 3084.4
## - ethnic_group:is_first_child             4     991.8 75740 3084.4
## <none>                                                74748 3084.6
## - lunch_type:is_first_child               1     261.5 75010 3084.7
## - parent_educ:practice_sport             10    2633.2 77381 3085.1
## - lunch_type:transport_means              1     319.1 75067 3085.2
## - ethnic_group:parent_marital_status     11    2959.1 77707 3085.5
## - parent_educ:parent_marital_status      15    4087.6 78836 3086.1
## - practice_sport:wkly_study_hours         4    1210.0 75958 3086.1
## + gender:transport_means                  1       3.1 74745 3086.6
## + test_prep:is_first_child                1       0.0 74748 3086.6
## + test_prep:parent_marital_status         2     221.4 74527 3086.9
## + is_first_child:wkly_study_hours         2     128.0 74620 3087.6
## + practice_sport:is_first_child           2      76.0 74672 3088.0
## + parent_educ:is_first_child              5     823.7 73924 3088.1
## + lunch_type:parent_marital_status        3     311.0 74437 3088.2
## - ethnic_group:lunch_type                 4    1480.1 76228 3088.2
## - lunch_type:wkly_study_hours             2    1018.3 75766 3088.6
## - lunch_type:practice_sport               2    1052.9 75801 3088.9
## + gender:ethnic_group                     4     449.4 74299 3089.1
## - ethnic_group:transport_means            4    1611.1 76359 3089.2
## + gender:parent_marital_status            3     126.5 74622 3089.6
## + parent_educ:transport_means             5     503.5 74245 3090.7
## + parent_marital_status:practice_sport    5     479.0 74269 3090.8
## + ethnic_group:practice_sport             8    1137.2 73611 3091.6
## + gender:parent_educ                      5     368.6 74379 3091.7
## + parent_educ:lunch_type                  5     256.9 74491 3092.6
## + parent_educ:test_prep                   5     215.5 74533 3092.9
## + parent_educ:wkly_study_hours           10    1202.3 73546 3095.1
## + ethnic_group:wkly_study_hours           8     551.9 74196 3096.3
## - parent_marital_status:wkly_study_hours  6    3151.6 77900 3097.0
## - parent_marital_status:is_first_child    3    2984.7 77733 3101.7
## + ethnic_group:parent_educ               20    2567.4 72181 3104.0
## 
## Step:  AIC=3082.66
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:test_prep                  4     771.6 75523 3080.7
## - transport_means:wkly_study_hours        2     273.4 75025 3080.8
## - lunch_type:test_prep                    1      20.5 74772 3080.8
## - practice_sport:transport_means          2     284.4 75036 3080.9
## - gender:test_prep                        1      31.3 74783 3080.9
## - parent_marital_status:transport_means   3     636.2 75388 3081.7
## - gender:is_first_child                   1     140.5 74892 3081.8
## - gender:wkly_study_hours                 2     428.0 75179 3082.0
## - test_prep:practice_sport                2     433.4 75185 3082.1
## - test_prep:wkly_study_hours              2     443.5 75195 3082.2
## - is_first_child:transport_means          1     195.4 74947 3082.2
## - test_prep:transport_means               1     211.2 74963 3082.3
## - gender:practice_sport                   2     475.6 75227 3082.4
## - ethnic_group:is_first_child             4     989.2 75741 3082.4
## <none>                                                74751 3082.7
## - lunch_type:is_first_child               1     264.5 75016 3082.8
## - parent_educ:practice_sport             10    2629.9 77381 3083.1
## - lunch_type:transport_means              1     323.5 75075 3083.2
## - ethnic_group:parent_marital_status     11    2960.2 77712 3083.6
## - parent_educ:parent_marital_status      15    4086.7 78838 3084.1
## - practice_sport:wkly_study_hours         4    1215.8 75967 3084.2
## + gender:lunch_type                       1       3.4 74748 3084.6
## + gender:transport_means                  1       3.2 74748 3084.6
## + test_prep:is_first_child                1       0.0 74751 3084.7
## + test_prep:parent_marital_status         2     220.7 74531 3084.9
## + is_first_child:wkly_study_hours         2     127.3 74624 3085.7
## + practice_sport:is_first_child           2      74.4 74677 3086.1
## + parent_educ:is_first_child              5     822.7 73929 3086.1
## + lunch_type:parent_marital_status        3     314.3 74437 3086.2
## - ethnic_group:lunch_type                 4    1480.8 76232 3086.2
## - lunch_type:wkly_study_hours             2    1015.8 75767 3086.6
## - lunch_type:practice_sport               2    1077.3 75829 3087.1
## + gender:ethnic_group                     4     446.2 74305 3087.1
## - ethnic_group:transport_means            4    1620.2 76372 3087.3
## + gender:parent_marital_status            3     125.2 74626 3087.7
## + parent_educ:transport_means             5     506.3 74245 3088.7
## + parent_marital_status:practice_sport    5     479.0 74272 3088.9
## + ethnic_group:practice_sport             8    1127.4 73624 3089.7
## + gender:parent_educ                      5     368.0 74383 3089.8
## + parent_educ:lunch_type                  5     259.4 74492 3090.6
## + parent_educ:test_prep                   5     213.8 74538 3091.0
## + parent_educ:wkly_study_hours           10    1201.5 73550 3093.1
## + ethnic_group:wkly_study_hours           8     551.4 74200 3094.3
## - parent_marital_status:wkly_study_hours  6    3192.1 77943 3095.3
## - parent_marital_status:is_first_child    3    2981.5 77733 3099.7
## + ethnic_group:parent_educ               20    2531.3 72220 3102.3
## 
## Step:  AIC=3080.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:test_prep                        1      11.2 75534 3078.8
## - transport_means:wkly_study_hours        2     278.8 75802 3078.9
## - lunch_type:test_prep                    1      35.1 75558 3079.0
## - practice_sport:transport_means          2     292.2 75815 3079.0
## - parent_marital_status:transport_means   3     569.2 76092 3079.2
## - gender:is_first_child                   1      97.8 75621 3079.5
## - test_prep:practice_sport                2     392.1 75915 3079.8
## - gender:wkly_study_hours                 2     415.8 75939 3080.0
## - is_first_child:transport_means          1     206.3 75729 3080.3
## - lunch_type:is_first_child               1     230.7 75754 3080.5
## - gender:practice_sport                   2     488.1 76011 3080.5
## - test_prep:transport_means               1     243.1 75766 3080.6
## <none>                                                75523 3080.7
## - ethnic_group:is_first_child             4    1039.2 76562 3080.8
## - ethnic_group:parent_marital_status     11    2923.8 78447 3081.1
## - test_prep:wkly_study_hours              2     590.8 76114 3081.3
## - lunch_type:transport_means              1     353.3 75876 3081.5
## - parent_educ:practice_sport             10    2734.4 78257 3081.7
## - parent_educ:parent_marital_status      15    4073.2 79596 3081.7
## - practice_sport:wkly_study_hours         4    1215.7 76739 3082.1
## + ethnic_group:test_prep                  4     771.6 74751 3082.7
## - ethnic_group:lunch_type                 4    1286.4 76809 3082.7
## + gender:lunch_type                       1       2.7 75520 3082.7
## + gender:transport_means                  1       2.1 75521 3082.7
## + test_prep:is_first_child                1       1.5 75522 3082.7
## + test_prep:parent_marital_status         2     233.9 75289 3082.9
## + is_first_child:wkly_study_hours         2     112.4 75411 3083.8
## + parent_educ:is_first_child              5     859.8 74663 3084.0
## + practice_sport:is_first_child           2      84.3 75439 3084.1
## + lunch_type:parent_marital_status        3     334.5 75188 3084.1
## - lunch_type:wkly_study_hours             2     995.9 76519 3084.4
## - ethnic_group:transport_means            4    1599.8 77123 3085.1
## + gender:parent_marital_status            3     137.8 75385 3085.6
## - lunch_type:practice_sport               2    1217.2 76740 3086.2
## + gender:ethnic_group                     4     290.9 75232 3086.4
## + parent_educ:transport_means             5     542.4 74981 3086.5
## + parent_marital_status:practice_sport    5     462.2 75061 3087.1
## + ethnic_group:practice_sport             8    1117.8 74405 3087.9
## + gender:parent_educ                      5     330.2 75193 3088.1
## + parent_educ:lunch_type                  5     277.0 75246 3088.6
## + parent_educ:test_prep                   5     146.2 75377 3089.6
## + parent_educ:wkly_study_hours           10    1155.0 74368 3091.6
## - parent_marital_status:wkly_study_hours  6    3000.9 78524 3091.7
## + ethnic_group:wkly_study_hours           8     559.8 74963 3092.3
## - parent_marital_status:is_first_child    3    3061.0 78584 3098.2
## + ethnic_group:parent_educ               20    2514.4 73009 3100.7
## 
## Step:  AIC=3078.81
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - transport_means:wkly_study_hours        2     273.8 75808 3076.9
## - practice_sport:transport_means          2     292.1 75826 3077.1
## - lunch_type:test_prep                    1      38.5 75573 3077.1
## - parent_marital_status:transport_means   3     575.3 76109 3077.3
## - gender:is_first_child                   1      93.4 75627 3077.5
## - test_prep:practice_sport                2     389.8 75924 3077.8
## - gender:wkly_study_hours                 2     432.6 75967 3078.2
## - is_first_child:transport_means          1     203.0 75737 3078.4
## - lunch_type:is_first_child               1     227.6 75762 3078.6
## - test_prep:transport_means               1     239.8 75774 3078.7
## - gender:practice_sport                   2     500.9 76035 3078.7
## <none>                                                75534 3078.8
## - ethnic_group:is_first_child             4    1033.7 76568 3078.8
## - test_prep:wkly_study_hours              2     583.8 76118 3079.3
## - ethnic_group:parent_marital_status     11    2952.3 78486 3079.4
## - lunch_type:transport_means              1     358.4 75893 3079.6
## - parent_educ:parent_marital_status      15    4062.5 79597 3079.7
## - parent_educ:practice_sport             10    2755.3 78289 3079.9
## - practice_sport:wkly_study_hours         4    1211.3 76745 3080.2
## + gender:test_prep                        1      11.2 75523 3080.7
## + gender:lunch_type                       1       2.2 75532 3080.8
## - ethnic_group:lunch_type                 4    1289.5 76824 3080.8
## + test_prep:is_first_child                1       1.4 75533 3080.8
## + gender:transport_means                  1       1.2 75533 3080.8
## + ethnic_group:test_prep                  4     751.4 74783 3080.9
## + test_prep:parent_marital_status         2     229.3 75305 3081.0
## + is_first_child:wkly_study_hours         2     113.7 75420 3081.9
## + parent_educ:is_first_child              5     858.1 74676 3082.1
## + practice_sport:is_first_child           2      86.3 75448 3082.1
## + lunch_type:parent_marital_status        3     338.3 75196 3082.2
## - lunch_type:wkly_study_hours             2    1005.4 76540 3082.6
## - ethnic_group:transport_means            4    1607.5 77142 3083.2
## + gender:parent_marital_status            3     142.5 75392 3083.7
## - lunch_type:practice_sport               2    1211.6 76746 3084.2
## + gender:ethnic_group                     4     285.8 75248 3084.6
## + parent_educ:transport_means             5     532.2 75002 3084.6
## + parent_marital_status:practice_sport    5     465.2 75069 3085.2
## + ethnic_group:practice_sport             8    1103.3 74431 3086.1
## + gender:parent_educ                      5     323.0 75211 3086.3
## + parent_educ:lunch_type                  5     280.5 75254 3086.6
## + parent_educ:test_prep                   5     151.5 75383 3087.6
## + parent_educ:wkly_study_hours           10    1155.9 74378 3089.7
## - parent_marital_status:wkly_study_hours  6    2990.8 78525 3089.7
## + ethnic_group:wkly_study_hours           8     568.8 74965 3090.3
## - parent_marital_status:is_first_child    3    3050.1 78584 3096.2
## + ethnic_group:parent_educ               20    2513.7 73020 3098.8
## 
## Step:  AIC=3076.94
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:test_prep                    1      37.1 75845 3075.2
## - parent_marital_status:transport_means   3     554.6 76363 3075.2
## - practice_sport:transport_means          2     311.7 76120 3075.4
## - gender:is_first_child                   1      96.6 75905 3075.7
## - gender:wkly_study_hours                 2     407.4 76215 3076.1
## - test_prep:practice_sport                2     424.4 76232 3076.2
## - is_first_child:transport_means          1     201.9 76010 3076.5
## - test_prep:transport_means               1     209.2 76017 3076.6
## - lunch_type:is_first_child               1     237.9 76046 3076.8
## - gender:practice_sport                   2     498.4 76306 3076.8
## - ethnic_group:parent_marital_status     11    2879.7 78688 3076.9
## <none>                                                75808 3076.9
## - ethnic_group:is_first_child             4    1044.5 76852 3077.0
## - parent_educ:practice_sport             10    2625.6 78434 3077.0
## - test_prep:wkly_study_hours              2     530.9 76339 3077.1
## - parent_educ:parent_marital_status      15    4007.1 79815 3077.3
## - lunch_type:transport_means              1     332.9 76141 3077.5
## - practice_sport:wkly_study_hours         4    1234.7 77043 3078.5
## + transport_means:wkly_study_hours        2     273.8 75534 3078.8
## + gender:test_prep                        1       6.2 75802 3078.9
## + gender:lunch_type                       1       1.6 75806 3078.9
## + gender:transport_means                  1       1.5 75806 3078.9
## - ethnic_group:lunch_type                 4    1295.3 77103 3078.9
## + test_prep:is_first_child                1       0.3 75808 3078.9
## + ethnic_group:test_prep                  4     760.2 75048 3079.0
## + test_prep:parent_marital_status         2     236.2 75572 3079.1
## + is_first_child:wkly_study_hours         2     128.6 75679 3079.9
## + lunch_type:parent_marital_status        3     366.5 75441 3080.1
## + parent_educ:is_first_child              5     860.6 74947 3080.2
## + practice_sport:is_first_child           2      86.9 75721 3080.3
## - lunch_type:wkly_study_hours             2    1028.6 76837 3080.9
## + gender:parent_marital_status            3     127.2 75681 3081.9
## - ethnic_group:transport_means            4    1734.7 77543 3082.3
## - lunch_type:practice_sport               2    1215.6 77024 3082.3
## + gender:ethnic_group                     4     306.9 75501 3082.6
## + parent_educ:transport_means             5     551.3 75257 3082.6
## + parent_marital_status:practice_sport    5     473.7 75334 3083.2
## + ethnic_group:practice_sport             8    1130.4 74677 3084.1
## + gender:parent_educ                      5     343.9 75464 3084.3
## + parent_educ:lunch_type                  5     307.8 75500 3084.5
## + parent_educ:test_prep                   5     146.0 75662 3085.8
## + parent_educ:wkly_study_hours           10    1197.1 74611 3087.6
## - parent_marital_status:wkly_study_hours  6    3056.3 78864 3088.3
## + ethnic_group:wkly_study_hours           8     470.4 75338 3089.3
## - parent_marital_status:is_first_child    3    2949.0 78757 3093.5
## + ethnic_group:parent_educ               20    2520.2 73288 3097.0
## 
## Step:  AIC=3075.23
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:transport_means   3     560.4 76405 3073.6
## - practice_sport:transport_means          2     322.3 76167 3073.7
## - gender:is_first_child                   1     101.3 75946 3074.0
## - gender:wkly_study_hours                 2     403.5 76249 3074.4
## - test_prep:practice_sport                2     429.6 76275 3074.6
## - is_first_child:transport_means          1     190.4 76035 3074.7
## - test_prep:transport_means               1     208.1 76053 3074.8
## - gender:practice_sport                   2     491.6 76337 3075.0
## - ethnic_group:parent_marital_status     11    2862.4 78707 3075.1
## - lunch_type:is_first_child               1     242.6 76088 3075.1
## <none>                                                75845 3075.2
## - test_prep:wkly_study_hours              2     526.9 76372 3075.3
## - ethnic_group:is_first_child             4    1053.8 76899 3075.4
## - parent_educ:practice_sport             10    2648.9 78494 3075.5
## - lunch_type:transport_means              1     311.6 76157 3075.7
## - parent_educ:parent_marital_status      15    4021.2 79866 3075.7
## + lunch_type:test_prep                    1      37.1 75808 3076.9
## - practice_sport:wkly_study_hours         4    1266.5 77111 3077.0
## + transport_means:wkly_study_hours        2     272.4 75573 3077.1
## + gender:test_prep                        1       8.6 75836 3077.2
## + ethnic_group:test_prep                  4     772.6 75072 3077.2
## + gender:lunch_type                       1       2.6 75842 3077.2
## + gender:transport_means                  1       1.9 75843 3077.2
## + test_prep:is_first_child                1       0.4 75845 3077.2
## + test_prep:parent_marital_status         2     236.9 75608 3077.4
## - ethnic_group:lunch_type                 4    1340.5 77186 3077.6
## + is_first_child:wkly_study_hours         2     137.2 75708 3078.2
## + lunch_type:parent_marital_status        3     366.8 75478 3078.4
## + practice_sport:is_first_child           2      91.2 75754 3078.5
## + parent_educ:is_first_child              5     842.0 75003 3078.7
## - lunch_type:wkly_study_hours             2    1005.4 76850 3079.0
## + gender:parent_marital_status            3     121.2 75724 3080.3
## - lunch_type:practice_sport               2    1201.8 77047 3080.5
## - ethnic_group:transport_means            4    1735.4 77580 3080.6
## + gender:ethnic_group                     4     317.8 75527 3080.8
## + parent_educ:transport_means             5     567.5 75278 3080.8
## + parent_marital_status:practice_sport    5     467.7 75377 3081.6
## + ethnic_group:practice_sport             8    1157.3 74688 3082.2
## + gender:parent_educ                      5     355.3 75490 3082.5
## + parent_educ:lunch_type                  5     301.9 75543 3082.9
## + parent_educ:test_prep                   5     144.0 75701 3084.1
## + parent_educ:wkly_study_hours           10    1215.6 74629 3085.7
## - parent_marital_status:wkly_study_hours  6    3086.6 78932 3086.8
## + ethnic_group:wkly_study_hours           8     482.4 75363 3087.5
## - parent_marital_status:is_first_child    3    2971.6 78817 3091.9
## + ethnic_group:parent_educ               20    2528.3 73317 3095.2
## 
## Step:  AIC=3073.57
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:transport_means          2     289.2 76695 3071.8
## - gender:is_first_child                   1     104.0 76509 3072.4
## - parent_educ:parent_marital_status      15    3830.4 80236 3072.4
## - gender:wkly_study_hours                 2     397.3 76803 3072.6
## - test_prep:practice_sport                2     408.6 76814 3072.7
## - ethnic_group:parent_marital_status     11    2815.5 79221 3072.9
## - gender:practice_sport                   2     469.1 76875 3073.2
## - test_prep:transport_means               1     227.5 76633 3073.3
## - lunch_type:is_first_child               1     235.1 76640 3073.4
## - test_prep:wkly_study_hours              2     513.5 76919 3073.5
## <none>                                                76405 3073.6
## - ethnic_group:is_first_child             4    1050.0 77455 3073.6
## - is_first_child:transport_means          1     266.4 76672 3073.6
## - lunch_type:transport_means              1     334.7 76740 3074.2
## - parent_educ:practice_sport             10    2736.7 79142 3074.3
## - practice_sport:wkly_study_hours         4    1246.9 77652 3075.1
## + test_prep:parent_marital_status         2     308.7 76097 3075.2
## + parent_marital_status:transport_means   3     560.4 75845 3075.2
## + lunch_type:test_prep                    1      42.8 76363 3075.2
## + gender:test_prep                        1      14.8 76391 3075.5
## + gender:lunch_type                       1       1.2 76404 3075.6
## + gender:transport_means                  1       1.0 76404 3075.6
## + test_prep:is_first_child                1       0.1 76405 3075.6
## + transport_means:wkly_study_hours        2     249.8 76156 3075.6
## - ethnic_group:lunch_type                 4    1321.6 77727 3075.7
## + ethnic_group:test_prep                  4     702.7 75703 3076.1
## + lunch_type:parent_marital_status        3     361.0 76044 3076.8
## + is_first_child:wkly_study_hours         2      83.7 76322 3076.9
## + practice_sport:is_first_child           2      61.6 76344 3077.1
## - lunch_type:wkly_study_hours             2    1054.0 77459 3077.7
## - ethnic_group:transport_means            4    1591.6 77997 3077.7
## + parent_educ:is_first_child              5     718.4 75687 3078.0
## + gender:parent_marital_status            3     187.7 76218 3078.1
## + gender:ethnic_group                     4     335.7 76070 3079.0
## - lunch_type:practice_sport               2    1274.9 77680 3079.3
## + parent_educ:transport_means             5     466.6 75939 3080.0
## + parent_marital_status:practice_sport    5     458.2 75947 3080.0
## + ethnic_group:practice_sport             8    1209.6 75196 3080.2
## + gender:parent_educ                      5     401.7 76004 3080.5
## + parent_educ:lunch_type                  5     307.1 76098 3081.2
## + parent_educ:test_prep                   5     119.6 76286 3082.7
## - parent_marital_status:wkly_study_hours  6    2935.7 79341 3083.8
## + parent_educ:wkly_study_hours           10    1232.7 75173 3084.0
## + ethnic_group:wkly_study_hours           8     494.3 75911 3085.8
## - parent_marital_status:is_first_child    3    3121.7 79527 3091.2
## + ethnic_group:parent_educ               20    2414.4 73991 3094.6
## 
## Step:  AIC=3071.8
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:parent_marital_status      15    3742.3 80437 3069.9
## - ethnic_group:parent_marital_status     11    2688.4 79383 3070.1
## - test_prep:practice_sport                2     378.6 77073 3070.7
## - gender:is_first_child                   1     134.4 76829 3070.8
## - gender:wkly_study_hours                 2     415.0 77109 3071.0
## - gender:practice_sport                   2     415.5 77110 3071.0
## - test_prep:transport_means               1     209.1 76904 3071.4
## - lunch_type:is_first_child               1     249.4 76944 3071.7
## - ethnic_group:is_first_child             4    1038.9 77733 3071.7
## - test_prep:wkly_study_hours              2     514.3 77209 3071.8
## <none>                                                76695 3071.8
## - parent_educ:practice_sport             10    2659.6 79354 3071.9
## - is_first_child:transport_means          1     324.1 77019 3072.3
## - lunch_type:transport_means              1     352.1 77047 3072.5
## - practice_sport:wkly_study_hours         4    1213.3 77908 3073.1
## + test_prep:parent_marital_status         2     318.9 76376 3073.3
## + lunch_type:test_prep                    1      53.6 76641 3073.4
## + practice_sport:transport_means          2     289.2 76405 3073.6
## - ethnic_group:lunch_type                 4    1283.1 77978 3073.6
## + gender:test_prep                        1      15.0 76680 3073.7
## + transport_means:wkly_study_hours        2     270.1 76424 3073.7
## + parent_marital_status:transport_means   3     527.2 76167 3073.7
## + gender:lunch_type                       1       2.2 76692 3073.8
## + gender:transport_means                  1       1.1 76693 3073.8
## + test_prep:is_first_child                1       0.2 76694 3073.8
## + ethnic_group:test_prep                  4     713.2 75981 3074.3
## + lunch_type:parent_marital_status        3     359.8 76335 3075.0
## + is_first_child:wkly_study_hours         2      90.4 76604 3075.1
## + practice_sport:is_first_child           2      60.5 76634 3075.3
## - lunch_type:wkly_study_hours             2    1032.8 77727 3075.7
## - ethnic_group:transport_means            4    1618.0 78313 3076.1
## + parent_educ:is_first_child              5     721.0 75974 3076.2
## + gender:parent_marital_status            3     164.7 76530 3076.5
## + gender:ethnic_group                     4     328.7 76366 3077.3
## - lunch_type:practice_sport               2    1255.8 77950 3077.4
## + parent_marital_status:practice_sport    5     444.6 76250 3078.4
## + ethnic_group:practice_sport             8    1203.1 75491 3078.5
## + parent_educ:transport_means             5     422.0 76273 3078.6
## + gender:parent_educ                      5     396.2 76298 3078.8
## + parent_educ:lunch_type                  5     370.5 76324 3078.9
## + parent_educ:test_prep                   5     141.0 76554 3080.7
## - parent_marital_status:wkly_study_hours  6    2936.1 79631 3082.0
## + parent_educ:wkly_study_hours           10    1143.1 75551 3082.9
## + ethnic_group:wkly_study_hours           8     499.7 76195 3083.9
## - parent_marital_status:is_first_child    3    3103.2 79798 3089.2
## + ethnic_group:parent_educ               20    2362.4 74332 3093.3
## 
## Step:  AIC=3069.91
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:practice_sport                2     252.6 80689 3067.8
## - ethnic_group:is_first_child             4     845.9 81283 3068.1
## - gender:wkly_study_hours                 2     337.8 80775 3068.4
## - ethnic_group:lunch_type                 4     964.9 81402 3068.9
## - gender:is_first_child                   1     152.4 80589 3069.0
## - gender:practice_sport                   2     443.1 80880 3069.2
## - test_prep:wkly_study_hours              2     487.4 80924 3069.5
## <none>                                                80437 3069.9
## - is_first_child:transport_means          1     291.8 80729 3070.1
## - ethnic_group:parent_marital_status     11    3119.9 83557 3070.4
## - test_prep:transport_means               1     338.9 80776 3070.4
## - practice_sport:wkly_study_hours         4    1165.6 81602 3070.4
## - lunch_type:is_first_child               1     392.2 80829 3070.8
## - lunch_type:transport_means              1     419.3 80856 3071.0
## - parent_educ:practice_sport             10    2963.0 83400 3071.2
## + lunch_type:test_prep                    1      63.2 80374 3071.4
## + parent_educ:parent_marital_status      15    3742.3 76695 3071.8
## + gender:transport_means                  1      14.0 80423 3071.8
## + gender:lunch_type                       1       1.8 80435 3071.9
## + gender:test_prep                        1       1.5 80435 3071.9
## + test_prep:is_first_child                1       0.2 80437 3071.9
## + transport_means:wkly_study_hours        2     233.9 80203 3072.2
## + practice_sport:transport_means          2     201.1 80236 3072.4
## + is_first_child:wkly_study_hours         2     171.6 80265 3072.7
## + ethnic_group:test_prep                  4     689.7 79747 3072.8
## + parent_marital_status:transport_means   3     369.7 80067 3073.2
## + lunch_type:parent_marital_status        3     335.5 80101 3073.4
## + practice_sport:is_first_child           2      26.1 80411 3073.7
## + test_prep:parent_marital_status         3     293.2 80144 3073.8
## + parent_educ:is_first_child              5     730.0 79707 3074.5
## - ethnic_group:transport_means            4    1749.2 82186 3074.6
## + gender:ethnic_group                     4     429.6 80007 3074.8
## - lunch_type:practice_sport               2    1226.7 81664 3074.8
## + gender:parent_educ                      5     654.3 79783 3075.1
## - lunch_type:wkly_study_hours             2    1303.3 81740 3075.4
## + parent_marital_status:practice_sport    6     872.2 79565 3075.5
## + gender:parent_marital_status            3      19.2 80418 3075.8
## + parent_educ:transport_means             5     433.9 80003 3076.7
## + parent_educ:lunch_type                  5     383.9 80053 3077.1
## + ethnic_group:practice_sport             8    1150.9 79286 3077.4
## - parent_marital_status:wkly_study_hours  6    2787.1 83224 3078.0
## + parent_educ:wkly_study_hours           10    1534.7 78902 3078.6
## + parent_educ:test_prep                   5     161.9 80275 3078.7
## + ethnic_group:wkly_study_hours           8     363.2 80074 3083.2
## - parent_marital_status:is_first_child    3    3025.4 83462 3085.7
## + ethnic_group:parent_educ               20    2639.7 77797 3090.2
## 
## Step:  AIC=3067.76
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:wkly_study_hours                 2     317.4 81007 3066.1
## - ethnic_group:is_first_child             4     876.0 81565 3066.1
## - gender:is_first_child                   1     149.2 80839 3066.8
## - ethnic_group:lunch_type                 4    1028.7 81718 3067.2
## - test_prep:wkly_study_hours              2     478.9 81168 3067.2
## - gender:practice_sport                   2     482.9 81172 3067.3
## <none>                                                80689 3067.8
## - is_first_child:transport_means          1     301.4 80991 3068.0
## - ethnic_group:parent_marital_status     11    3122.9 83812 3068.2
## - test_prep:transport_means               1     362.3 81052 3068.4
## - practice_sport:wkly_study_hours         4    1204.8 81894 3068.5
## - lunch_type:transport_means              1     401.7 81091 3068.7
## - lunch_type:is_first_child               1     414.9 81104 3068.8
## - parent_educ:practice_sport             10    2989.8 83679 3069.2
## + lunch_type:test_prep                    1      68.9 80620 3069.3
## + gender:transport_means                  1      16.0 80673 3069.6
## + gender:lunch_type                       1       3.0 80686 3069.7
## + gender:test_prep                        1       0.9 80689 3069.8
## + test_prep:is_first_child                1       0.5 80689 3069.8
## + test_prep:practice_sport                2     252.6 80437 3069.9
## + transport_means:wkly_study_hours        2     250.9 80439 3069.9
## + practice_sport:transport_means          2     179.0 80510 3070.4
## + parent_educ:parent_marital_status      15    3616.3 77073 3070.7
## + is_first_child:wkly_study_hours         2     142.8 80547 3070.7
## + ethnic_group:test_prep                  4     679.6 80010 3070.8
## + parent_marital_status:transport_means   3     354.1 80335 3071.2
## + lunch_type:parent_marital_status        3     344.3 80345 3071.2
## + test_prep:parent_marital_status         3     342.7 80347 3071.2
## + practice_sport:is_first_child           2      29.2 80660 3071.6
## + parent_educ:is_first_child              5     816.0 79873 3071.8
## - ethnic_group:transport_means            4    1694.6 82384 3072.0
## + gender:parent_educ                      5     703.6 79986 3072.6
## + gender:ethnic_group                     4     422.9 80266 3072.7
## + parent_marital_status:practice_sport    6     896.9 79792 3073.2
## - lunch_type:practice_sport               2    1303.1 81992 3073.2
## + gender:parent_marital_status            3      35.1 80654 3073.5
## - lunch_type:wkly_study_hours             2    1383.7 82073 3073.8
## + parent_educ:transport_means             5     451.8 80238 3074.4
## + parent_educ:lunch_type                  5     429.1 80260 3074.6
## - parent_marital_status:wkly_study_hours  6    2769.9 83459 3075.7
## + ethnic_group:practice_sport             8    1090.2 79599 3075.7
## + parent_educ:wkly_study_hours           10    1608.6 79081 3075.9
## + parent_educ:test_prep                   5     143.5 80546 3076.7
## + ethnic_group:wkly_study_hours           8     358.2 80331 3081.1
## - parent_marital_status:is_first_child    3    3049.0 83738 3083.6
## + ethnic_group:parent_educ               20    2713.0 77976 3087.6
## 
## Step:  AIC=3066.08
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:practice_sport + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:is_first_child             4     824.9 81832 3064.1
## - gender:is_first_child                   1     157.3 81164 3065.2
## - test_prep:wkly_study_hours              2     469.7 81477 3065.5
## - ethnic_group:lunch_type                 4    1034.1 82041 3065.6
## - gender:practice_sport                   2     527.0 81534 3065.9
## - is_first_child:transport_means          1     270.8 81278 3066.1
## <none>                                                81007 3066.1
## - ethnic_group:parent_marital_status     11    3080.5 84087 3066.1
## - practice_sport:wkly_study_hours         4    1177.4 82184 3066.6
## - test_prep:transport_means               1     371.6 81378 3066.8
## - lunch_type:is_first_child               1     398.6 81405 3067.0
## - lunch_type:transport_means              1     411.4 81418 3067.1
## + lunch_type:test_prep                    1      65.7 80941 3067.6
## + gender:wkly_study_hours                 2     317.4 80689 3067.8
## - parent_educ:practice_sport             10    3056.9 84064 3067.9
## + gender:transport_means                  1      14.9 80992 3068.0
## + gender:test_prep                        1       6.9 81000 3068.0
## + test_prep:is_first_child                1       4.0 81003 3068.1
## + gender:lunch_type                       1       1.5 81005 3068.1
## + test_prep:practice_sport                2     232.2 80775 3068.4
## + transport_means:wkly_study_hours        2     227.6 80779 3068.4
## + practice_sport:transport_means          2     188.6 80818 3068.7
## + is_first_child:wkly_study_hours         2     133.4 80873 3069.1
## + ethnic_group:test_prep                  4     673.4 80333 3069.2
## + test_prep:parent_marital_status         3     361.5 80645 3069.4
## + parent_marital_status:transport_means   3     350.5 80656 3069.5
## + parent_educ:parent_marital_status      15    3542.0 77465 3069.7
## + practice_sport:is_first_child           2      23.4 80983 3069.9
## + lunch_type:parent_marital_status        3     291.6 80715 3069.9
## - ethnic_group:transport_means            4    1664.0 82671 3070.1
## + parent_educ:is_first_child              5     765.7 80241 3070.5
## + gender:ethnic_group                     4     458.3 80549 3070.7
## + gender:parent_educ                      5     716.2 80291 3070.8
## - lunch_type:wkly_study_hours             2    1298.7 82306 3071.5
## + parent_marital_status:practice_sport    6     903.1 80104 3071.5
## - lunch_type:practice_sport               2    1320.2 82327 3071.6
## + gender:parent_marital_status            3      51.8 80955 3071.7
## + parent_educ:transport_means             5     408.3 80598 3073.1
## + parent_educ:wkly_study_hours           10    1753.4 79253 3073.2
## + parent_educ:lunch_type                  5     387.2 80620 3073.2
## + ethnic_group:practice_sport             8    1147.0 79860 3073.7
## + parent_educ:test_prep                   5     166.8 80840 3074.9
## - parent_marital_status:wkly_study_hours  6    3058.9 84066 3075.9
## + ethnic_group:wkly_study_hours           8     326.3 80680 3079.7
## - parent_marital_status:is_first_child    3    2917.4 83924 3080.9
## + ethnic_group:parent_educ               20    2718.5 78288 3085.9
## 
## Step:  AIC=3064.06
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:lunch_type                 4     852.1 82684 3062.2
## - ethnic_group:parent_marital_status     11    2845.2 84677 3062.2
## - test_prep:wkly_study_hours              2     337.2 82169 3062.5
## - gender:is_first_child                   1      92.9 81925 3062.7
## - is_first_child:transport_means          1     144.4 81976 3063.1
## - gender:practice_sport                   2     513.8 82346 3063.8
## <none>                                                81832 3064.1
## - test_prep:transport_means               1     331.1 82163 3064.4
## - lunch_type:transport_means              1     353.6 82185 3064.6
## - practice_sport:wkly_study_hours         4    1203.5 83035 3064.7
## + lunch_type:test_prep                    1      70.7 81761 3065.6
## - parent_educ:practice_sport             10    3037.2 84869 3065.6
## - lunch_type:is_first_child               1     516.8 82349 3065.8
## + test_prep:is_first_child                1      12.1 81820 3066.0
## + gender:transport_means                  1      11.6 81820 3066.0
## + gender:test_prep                        1       3.5 81828 3066.0
## + gender:lunch_type                       1       1.2 81830 3066.1
## + ethnic_group:is_first_child             4     824.9 81007 3066.1
## + test_prep:practice_sport                2     268.1 81564 3066.1
## + gender:wkly_study_hours                 2     266.2 81565 3066.1
## + transport_means:wkly_study_hours        2     249.9 81582 3066.2
## + is_first_child:wkly_study_hours         2     194.0 81638 3066.7
## + practice_sport:transport_means          2     186.5 81645 3066.7
## + ethnic_group:test_prep                  4     728.6 81103 3066.8
## + test_prep:parent_marital_status         3     433.6 81398 3066.9
## + parent_marital_status:transport_means   3     351.9 81480 3067.5
## + practice_sport:is_first_child           2      25.3 81806 3067.9
## + lunch_type:parent_marital_status        3     240.0 81592 3068.3
## + parent_educ:is_first_child              5     786.2 81046 3068.4
## + gender:ethnic_group                     4     454.0 81378 3068.8
## - lunch_type:wkly_study_hours             2    1224.7 83056 3068.8
## + gender:parent_educ                      5     703.5 81128 3069.0
## + parent_educ:parent_marital_status      15    3382.9 78449 3069.2
## - lunch_type:practice_sport               2    1335.5 83167 3069.6
## + parent_marital_status:practice_sport    6     882.2 80950 3069.7
## - ethnic_group:transport_means            4    1911.7 83743 3069.7
## + gender:parent_marital_status            3      35.0 81797 3069.8
## + parent_educ:wkly_study_hours           10    1830.4 80001 3070.7
## + parent_educ:transport_means             5     445.2 81387 3070.8
## + parent_educ:lunch_type                  5     377.7 81454 3071.3
## + ethnic_group:practice_sport             8    1069.7 80762 3072.3
## + parent_educ:test_prep                   5     160.9 81671 3072.9
## - parent_marital_status:wkly_study_hours  6    2994.3 84826 3073.3
## - parent_marital_status:is_first_child    3    2566.9 84399 3076.3
## + ethnic_group:wkly_study_hours           8     354.1 81478 3077.5
## + ethnic_group:parent_educ               20    2784.5 79047 3083.6
## 
## Step:  AIC=3062.17
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + ethnic_group:parent_marital_status + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_marital_status     11   2792.28 85476 3059.8
## - test_prep:wkly_study_hours              2    332.30 83016 3060.5
## - gender:is_first_child                   1     84.77 82769 3060.8
## - is_first_child:transport_means          1    122.86 82807 3061.0
## - gender:practice_sport                   2    436.01 83120 3061.3
## - practice_sport:wkly_study_hours         4   1064.27 83748 3061.7
## <none>                                                82684 3062.2
## - test_prep:transport_means               1    367.25 83051 3062.8
## - lunch_type:transport_means              1    416.94 83101 3063.1
## + lunch_type:test_prep                    1    106.82 82577 3063.4
## - lunch_type:is_first_child               1    457.20 83141 3063.4
## + test_prep:practice_sport                2    327.08 82357 3063.8
## - parent_educ:practice_sport             10   3101.14 85785 3063.9
## + ethnic_group:lunch_type                 4    852.14 81832 3064.1
## + gender:transport_means                  1     14.86 82669 3064.1
## + test_prep:is_first_child                1      5.78 82678 3064.1
## + gender:lunch_type                       1      5.44 82678 3064.1
## + gender:test_prep                        1      4.70 82679 3064.1
## + gender:wkly_study_hours                 2    272.64 82411 3064.2
## + transport_means:wkly_study_hours        2    254.90 82429 3064.3
## + is_first_child:wkly_study_hours         2    193.27 82491 3064.8
## + test_prep:parent_marital_status         3    449.82 82234 3064.9
## + practice_sport:transport_means          2    155.79 82528 3065.1
## + ethnic_group:is_first_child             4    642.90 82041 3065.6
## + parent_marital_status:transport_means   3    349.67 82334 3065.7
## + practice_sport:is_first_child           2     33.45 82650 3065.9
## + ethnic_group:test_prep                  4    566.41 82117 3066.1
## + parent_educ:is_first_child              5    839.05 81845 3066.2
## - lunch_type:wkly_study_hours             2   1133.23 83817 3066.2
## + lunch_type:parent_marital_status        3    269.52 82414 3066.2
## + gender:ethnic_group                     4    456.00 82228 3066.9
## - ethnic_group:transport_means            4   1846.35 84530 3067.2
## + parent_marital_status:practice_sport    6    954.98 81729 3067.3
## + gender:parent_educ                      5    616.92 82067 3067.8
## + gender:parent_marital_status            3     37.83 82646 3067.9
## + parent_educ:transport_means             5    525.02 82159 3068.4
## - lunch_type:practice_sport               2   1543.54 84227 3069.1
## + parent_educ:parent_marital_status      15   3130.53 79553 3069.4
## + ethnic_group:practice_sport             8   1213.72 81470 3069.4
## + parent_educ:lunch_type                  5    340.93 82343 3069.7
## + parent_educ:test_prep                   5    161.91 82522 3071.0
## + parent_educ:wkly_study_hours           10   1527.60 81156 3071.2
## - parent_marital_status:wkly_study_hours  6   3050.50 85734 3071.5
## - parent_marital_status:is_first_child    3   2646.16 85330 3074.8
## + ethnic_group:wkly_study_hours           8    326.65 82357 3075.8
## + ethnic_group:parent_educ               20   2852.94 79831 3081.4
## 
## Step:  AIC=3059.76
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:is_first_child                   1      99.6 85576 3058.4
## - practice_sport:wkly_study_hours         4    1008.6 86485 3058.7
## - test_prep:wkly_study_hours              2     479.0 85955 3059.1
## - is_first_child:transport_means          1     198.2 85674 3059.1
## - gender:practice_sport                   2     564.4 86041 3059.7
## <none>                                                85476 3059.8
## - lunch_type:is_first_child               1     308.3 85784 3059.9
## - parent_educ:practice_sport             10    2978.9 88455 3060.0
## - test_prep:transport_means               1     364.2 85840 3060.3
## - lunch_type:transport_means              1     417.7 85894 3060.6
## + test_prep:practice_sport                2     328.5 85148 3061.5
## + lunch_type:test_prep                    1      32.5 85444 3061.5
## + gender:test_prep                        1      14.8 85461 3061.7
## + test_prep:is_first_child                1       1.7 85474 3061.8
## + gender:lunch_type                       1       0.3 85476 3061.8
## + gender:transport_means                  1       0.0 85476 3061.8
## + transport_means:wkly_study_hours        2     244.4 85232 3062.1
## + gender:wkly_study_hours                 2     237.4 85239 3062.1
## + ethnic_group:parent_marital_status     11    2792.3 82684 3062.2
## + ethnic_group:lunch_type                 4     799.3 84677 3062.2
## + practice_sport:transport_means          2     103.1 85373 3063.1
## + parent_marital_status:transport_means   3     372.4 85104 3063.2
## - lunch_type:wkly_study_hours             2    1083.0 86559 3063.2
## + is_first_child:wkly_study_hours         2      80.1 85396 3063.2
## + lunch_type:parent_marital_status        3     364.8 85111 3063.2
## + test_prep:parent_marital_status         3     353.5 85123 3063.3
## + parent_educ:parent_marital_status      15    3706.0 81770 3063.6
## + practice_sport:is_first_child           2      15.9 85460 3063.7
## - ethnic_group:transport_means            4    1765.3 87241 3063.8
## + ethnic_group:test_prep                  4     491.6 84985 3064.4
## + parent_marital_status:practice_sport    6    1039.9 84436 3064.5
## + parent_educ:is_first_child              5     744.1 84732 3064.6
## + gender:parent_marital_status            3     152.7 85323 3064.7
## + ethnic_group:is_first_child             4     412.6 85064 3064.9
## + gender:ethnic_group                     4     376.8 85099 3065.2
## - parent_marital_status:wkly_study_hours  6    2624.6 88101 3065.6
## + parent_educ:transport_means             5     566.9 84909 3065.8
## + parent_educ:wkly_study_hours           10    1851.9 83624 3066.8
## + gender:parent_educ                      5     421.5 85055 3066.8
## + ethnic_group:practice_sport             8    1241.8 84234 3067.1
## - lunch_type:practice_sport               2    1699.0 87175 3067.4
## + parent_educ:lunch_type                  5     306.9 85169 3067.6
## - parent_marital_status:is_first_child    3    2204.5 87681 3068.8
## + parent_educ:test_prep                   5     128.8 85347 3068.9
## + ethnic_group:wkly_study_hours           8     315.5 85161 3073.6
## + ethnic_group:parent_educ               20    2736.0 82740 3080.6
## 
## Step:  AIC=3058.45
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:wkly_study_hours              2     466.5 86042 3057.7
## - practice_sport:wkly_study_hours         4    1055.8 86632 3057.7
## - is_first_child:transport_means          1     187.3 85763 3057.7
## - lunch_type:is_first_child               1     290.5 85866 3058.4
## <none>                                                85576 3058.4
## - gender:practice_sport                   2     587.3 86163 3058.5
## - test_prep:transport_means               1     362.2 85938 3058.9
## - parent_educ:practice_sport             10    3073.1 88649 3059.3
## - lunch_type:transport_means              1     454.6 86030 3059.6
## + gender:is_first_child                   1      99.6 85476 3059.8
## + lunch_type:test_prep                    1      36.7 85539 3060.2
## + test_prep:practice_sport                2     321.6 85254 3060.2
## + gender:test_prep                        1      10.1 85566 3060.4
## + test_prep:is_first_child                1       3.9 85572 3060.4
## + gender:lunch_type                       1       0.3 85575 3060.4
## + gender:transport_means                  1       0.0 85576 3060.4
## + ethnic_group:parent_marital_status     11    2807.1 82769 3060.8
## + gender:wkly_study_hours                 2     239.8 85336 3060.8
## + transport_means:wkly_study_hours        2     235.6 85340 3060.8
## + ethnic_group:lunch_type                 4     790.3 84785 3061.0
## + practice_sport:transport_means          2     119.8 85456 3061.6
## - lunch_type:wkly_study_hours             2    1069.3 86645 3061.8
## + is_first_child:wkly_study_hours         2      93.1 85483 3061.8
## + parent_marital_status:transport_means   3     378.6 85197 3061.8
## + lunch_type:parent_marital_status        3     373.1 85203 3061.9
## + test_prep:parent_marital_status         3     366.2 85210 3061.9
## + practice_sport:is_first_child           2      17.0 85559 3062.3
## + parent_educ:parent_marital_status      15    3677.7 81898 3062.5
## - ethnic_group:transport_means            4    1832.9 87409 3062.9
## + ethnic_group:test_prep                  4     469.5 85106 3063.2
## + parent_educ:is_first_child              5     746.7 84829 3063.3
## + gender:parent_marital_status            3     164.8 85411 3063.3
## + parent_marital_status:practice_sport    6    1021.0 84555 3063.4
## + gender:ethnic_group                     4     396.7 85179 3063.7
## - parent_marital_status:wkly_study_hours  6    2559.8 88136 3063.8
## + ethnic_group:is_first_child             4     373.2 85203 3063.9
## + parent_educ:transport_means             5     547.7 85028 3064.7
## + parent_educ:wkly_study_hours           10    1883.7 83692 3065.3
## + gender:parent_educ                      5     423.0 85153 3065.5
## + parent_educ:lunch_type                  5     345.4 85230 3066.1
## + ethnic_group:practice_sport             8    1193.1 84383 3066.2
## - lunch_type:practice_sport               2    1747.0 87323 3066.4
## - parent_marital_status:is_first_child    3    2145.8 87722 3067.1
## + parent_educ:test_prep                   5     132.8 85443 3067.5
## + ethnic_group:wkly_study_hours           8     314.1 85262 3072.3
## + ethnic_group:parent_educ               20    2622.3 82953 3080.1
## 
## Step:  AIC=3057.66
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - is_first_child:transport_means          1     180.8 86223 3056.9
## - practice_sport:wkly_study_hours         4    1089.4 87132 3057.1
## - parent_educ:practice_sport             10    2918.5 88961 3057.3
## - lunch_type:is_first_child               1     245.9 86288 3057.3
## - gender:practice_sport                   2     569.1 86611 3057.6
## <none>                                                86042 3057.7
## - test_prep:transport_means               1     322.8 86365 3057.9
## - lunch_type:transport_means              1     347.8 86390 3058.0
## + test_prep:wkly_study_hours              2     466.5 85576 3058.4
## + ethnic_group:parent_marital_status     11    2953.0 83089 3059.1
## + gender:is_first_child                   1      87.1 85955 3059.1
## + lunch_type:test_prep                    1      28.5 86014 3059.5
## + test_prep:practice_sport                2     315.9 85726 3059.5
## + gender:test_prep                        1       3.7 86039 3059.6
## + test_prep:is_first_child                1       2.4 86040 3059.6
## + gender:lunch_type                       1       0.5 86042 3059.7
## + gender:transport_means                  1       0.1 86042 3059.7
## + gender:wkly_study_hours                 2     231.2 85811 3060.1
## + transport_means:wkly_study_hours        2     203.4 85839 3060.3
## + ethnic_group:lunch_type                 4     765.9 85276 3060.4
## + practice_sport:transport_means          2     121.1 85921 3060.8
## + is_first_child:wkly_study_hours         2      80.3 85962 3061.1
## + parent_marital_status:transport_means   3     367.4 85675 3061.1
## + test_prep:parent_marital_status         3     353.3 85689 3061.2
## + lunch_type:parent_marital_status        3     351.9 85690 3061.2
## - lunch_type:wkly_study_hours             2    1130.2 87172 3061.4
## + practice_sport:is_first_child           2      22.1 86020 3061.5
## - ethnic_group:transport_means            4    1762.4 87805 3061.6
## + ethnic_group:test_prep                  4     563.0 85479 3061.8
## + parent_educ:parent_marital_status      15    3637.1 82405 3062.2
## + parent_educ:is_first_child              5     782.3 85260 3062.3
## + parent_marital_status:practice_sport    6    1062.0 84980 3062.3
## + gender:parent_marital_status            3     132.6 85910 3062.8
## + gender:ethnic_group                     4     414.5 85628 3062.8
## - parent_marital_status:wkly_study_hours  6    2558.9 88601 3062.9
## + parent_educ:wkly_study_hours           10    2045.6 83997 3063.5
## + parent_educ:transport_means             5     565.0 85477 3063.8
## + ethnic_group:is_first_child             4     274.4 85768 3063.8
## + gender:parent_educ                      5     469.8 85572 3064.4
## - lunch_type:practice_sport               2    1596.3 87639 3064.5
## + parent_educ:lunch_type                  5     353.9 85688 3065.2
## + ethnic_group:practice_sport             8    1091.5 84951 3066.1
## - parent_marital_status:is_first_child    3    2170.7 88213 3066.4
## + parent_educ:test_prep                   5     135.1 85907 3066.7
## + ethnic_group:wkly_study_hours           8     351.6 85691 3071.2
## + ethnic_group:parent_educ               20    2649.4 83393 3079.2
## 
## Step:  AIC=3056.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:practice_sport             10    2832.5 89055 3056.0
## - practice_sport:wkly_study_hours         4    1063.9 87287 3056.1
## - lunch_type:is_first_child               1     244.7 86468 3056.6
## <none>                                                86223 3056.9
## - gender:practice_sport                   2     601.5 86825 3057.0
## - lunch_type:transport_means              1     345.2 86568 3057.2
## - test_prep:transport_means               1     351.2 86574 3057.3
## + is_first_child:transport_means          1     180.8 86042 3057.7
## + test_prep:wkly_study_hours              2     459.9 85763 3057.7
## + ethnic_group:parent_marital_status     11    3020.0 83203 3057.9
## + gender:is_first_child                   1      77.2 86146 3058.4
## + test_prep:practice_sport                2     317.0 85906 3058.7
## + lunch_type:test_prep                    1      18.6 86204 3058.8
## + test_prep:is_first_child                1       4.4 86219 3058.9
## + gender:test_prep                        1       2.5 86221 3058.9
## + gender:transport_means                  1       1.6 86221 3058.9
## + gender:lunch_type                       1       0.0 86223 3058.9
## + gender:wkly_study_hours                 2     214.7 86008 3059.4
## + transport_means:wkly_study_hours        2     201.8 86021 3059.5
## + ethnic_group:lunch_type                 4     760.6 85462 3059.7
## + practice_sport:transport_means          2     138.2 86085 3059.9
## + parent_marital_status:transport_means   3     425.2 85798 3060.0
## + is_first_child:wkly_study_hours         2      66.5 86156 3060.4
## + test_prep:parent_marital_status         3     354.6 85868 3060.5
## + lunch_type:parent_marital_status        3     348.9 85874 3060.5
## + practice_sport:is_first_child           2      15.4 86208 3060.8
## - ethnic_group:transport_means            4    1773.5 87996 3060.9
## + ethnic_group:test_prep                  4     562.5 85660 3061.0
## - lunch_type:wkly_study_hours             2    1200.3 87423 3061.1
## + parent_educ:is_first_child              5     810.7 85412 3061.3
## + parent_educ:parent_marital_status      15    3644.1 82579 3061.4
## + parent_marital_status:practice_sport    6    1060.8 85162 3061.6
## + gender:ethnic_group                     4     447.2 85776 3061.8
## - parent_marital_status:wkly_study_hours  6    2529.8 88753 3062.0
## + gender:parent_marital_status            3     115.9 86107 3062.1
## + parent_educ:wkly_study_hours           10    2054.9 84168 3062.7
## + parent_educ:transport_means             5     527.1 85696 3063.3
## - lunch_type:practice_sport               2    1567.4 87790 3063.5
## + ethnic_group:is_first_child             4     198.1 86025 3063.5
## + gender:parent_educ                      5     456.3 85767 3063.8
## + parent_educ:lunch_type                  5     338.7 85884 3064.6
## + ethnic_group:practice_sport             8    1146.4 85077 3065.0
## - parent_marital_status:is_first_child    3    2120.8 88344 3065.2
## + parent_educ:test_prep                   5     168.1 86055 3065.7
## + ethnic_group:wkly_study_hours           8     368.5 85854 3070.4
## + ethnic_group:parent_educ               20    2575.7 83647 3079.0
## 
## Step:  AIC=3055.97
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:wkly_study_hours         4     914.5 89970 3054.0
## - gender:practice_sport                   2     409.2 89465 3054.7
## - lunch_type:is_first_child               1     155.2 89211 3055.0
## <none>                                                89055 3056.0
## - lunch_type:transport_means              1     306.2 89362 3056.0
## - test_prep:transport_means               1     380.6 89436 3056.5
## + gender:is_first_child                   1     165.2 88890 3056.9
## + parent_educ:practice_sport             10    2832.5 86223 3056.9
## + is_first_child:transport_means          1      94.7 88961 3057.3
## + lunch_type:test_prep                    1      36.5 89019 3057.7
## + gender:test_prep                        1      19.6 89036 3057.8
## + gender:transport_means                  1      16.0 89039 3057.9
## + test_prep:wkly_study_hours              2     307.5 88748 3057.9
## + gender:lunch_type                       1       5.0 89050 3057.9
## + test_prep:is_first_child                1       2.3 89053 3057.9
## + gender:wkly_study_hours                 2     281.6 88774 3058.1
## + test_prep:practice_sport                2     274.1 88781 3058.2
## + parent_marital_status:transport_means   3     536.1 88519 3058.4
## + parent_educ:is_first_child              5    1120.5 87935 3058.5
## + ethnic_group:parent_marital_status     11    2866.7 86189 3058.7
## + parent_educ:parent_marital_status      15    4025.6 85030 3058.7
## + practice_sport:transport_means          2     128.4 88927 3059.1
## + ethnic_group:lunch_type                 4     727.7 88328 3059.1
## + transport_means:wkly_study_hours        2      91.2 88964 3059.4
## + test_prep:parent_marital_status         3     363.7 88692 3059.6
## + is_first_child:wkly_study_hours         2      59.9 88996 3059.6
## - parent_marital_status:wkly_study_hours  6    2422.9 91478 3059.8
## - lunch_type:wkly_study_hours             2    1192.1 90248 3059.8
## + ethnic_group:test_prep                  4     620.7 88435 3059.8
## + practice_sport:is_first_child           2      13.6 89042 3059.9
## + lunch_type:parent_marital_status        3     260.3 88795 3060.2
## - ethnic_group:transport_means            4    1888.2 90944 3060.3
## - lunch_type:practice_sport               2    1306.9 90362 3060.6
## + gender:ethnic_group                     4     493.9 88561 3060.7
## + gender:parent_marital_status            3     188.4 88867 3060.7
## + parent_educ:wkly_study_hours           10    2257.7 86798 3060.8
## + parent_marital_status:practice_sport    6     871.7 88184 3062.2
## + ethnic_group:is_first_child             4     259.4 88796 3062.2
## + parent_educ:transport_means             5     535.3 88520 3062.4
## + ethnic_group:practice_sport             8    1361.2 87694 3062.9
## + gender:parent_educ                      5     452.5 88603 3063.0
## - parent_marital_status:is_first_child    3    2116.2 91172 3063.8
## + parent_educ:lunch_type                  5     311.0 88744 3063.9
## + parent_educ:test_prep                   5     246.7 88809 3064.3
## + ethnic_group:wkly_study_hours           8     414.2 88641 3069.2
## + ethnic_group:parent_educ               20    2184.6 86871 3081.3
## - parent_educ                             5    6212.6 95268 3085.8
## 
## Step:  AIC=3053.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:is_first_child               1     104.8 90075 3052.7
## - gender:practice_sport                   2     480.0 90450 3053.1
## - lunch_type:transport_means              1     253.2 90223 3053.7
## <none>                                                89970 3054.0
## - test_prep:transport_means               1     362.9 90333 3054.4
## + gender:is_first_child                   1     220.7 89749 3054.5
## + is_first_child:transport_means          1      78.8 89891 3055.5
## + lunch_type:test_prep                    1      55.0 89915 3055.6
## + test_prep:wkly_study_hours              2     329.5 89640 3055.8
## + gender:test_prep                        1      17.9 89952 3055.9
## + test_prep:is_first_child                1       8.8 89961 3055.9
## + gender:transport_means                  1       6.2 89964 3055.9
## + practice_sport:wkly_study_hours         4     914.5 89055 3056.0
## + gender:lunch_type                       1       3.0 89967 3056.0
## + test_prep:practice_sport                2     288.9 89681 3056.1
## + parent_educ:practice_sport             10    2683.0 87287 3056.1
## + gender:wkly_study_hours                 2     260.5 89709 3056.3
## + parent_marital_status:transport_means   3     536.5 89433 3056.5
## - ethnic_group:transport_means            4    1731.1 91701 3057.2
## + transport_means:wkly_study_hours        2     106.2 89864 3057.3
## + practice_sport:transport_means          2     105.7 89864 3057.3
## + is_first_child:wkly_study_hours         2     105.5 89864 3057.3
## - lunch_type:wkly_study_hours             2    1121.3 91091 3057.3
## + parent_educ:parent_marital_status      15    3959.8 86010 3057.4
## + parent_educ:is_first_child              5     962.3 89008 3057.7
## + ethnic_group:parent_marital_status     11    2751.1 87219 3057.7
## + test_prep:parent_marital_status         3     339.8 89630 3057.8
## + ethnic_group:test_prep                  4     625.2 89345 3057.9
## + practice_sport:is_first_child           2      16.4 89954 3057.9
## + ethnic_group:lunch_type                 4     613.6 89356 3058.0
## - lunch_type:practice_sport               2    1223.0 91193 3058.0
## + gender:ethnic_group                     4     541.3 89429 3058.4
## - parent_marital_status:wkly_study_hours  6    2566.6 92537 3058.6
## + gender:parent_marital_status            3     213.7 89756 3058.6
## + lunch_type:parent_marital_status        3     185.9 89784 3058.8
## + parent_educ:wkly_study_hours           10    2163.2 87807 3059.6
## + ethnic_group:is_first_child             4     308.4 89662 3060.0
## + parent_educ:transport_means             5     606.4 89364 3060.0
## + parent_marital_status:practice_sport    6     804.4 89166 3060.7
## + gender:parent_educ                      5     467.2 89503 3060.9
## + ethnic_group:practice_sport             8    1351.5 88618 3061.1
## - parent_marital_status:is_first_child    3    2027.1 91997 3061.1
## + parent_educ:lunch_type                  5     369.3 89601 3061.6
## + parent_educ:test_prep                   5     264.7 89705 3062.3
## + ethnic_group:wkly_study_hours           8     442.1 89528 3067.1
## + ethnic_group:parent_educ               20    2078.3 87892 3080.2
## - parent_educ                             5    6298.3 96268 3083.9
## 
## Step:  AIC=3052.68
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + lunch_type:practice_sport + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:transport_means + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:practice_sport                   2     526.0 90601 3052.1
## - lunch_type:transport_means              1     243.3 90318 3052.3
## <none>                                                90075 3052.7
## - test_prep:transport_means               1     340.3 90415 3052.9
## + gender:is_first_child                   1     202.2 89873 3053.3
## + lunch_type:is_first_child               1     104.8 89970 3054.0
## + is_first_child:transport_means          1      77.3 89997 3054.2
## + lunch_type:test_prep                    1      62.2 90012 3054.3
## + gender:test_prep                        1      14.6 90060 3054.6
## + test_prep:is_first_child                1      11.9 90063 3054.6
## + gender:transport_means                  1       3.2 90072 3054.7
## + gender:lunch_type                       1       2.1 90073 3054.7
## + test_prep:wkly_study_hours              2     305.6 89769 3054.7
## + test_prep:practice_sport                2     299.1 89776 3054.7
## + practice_sport:wkly_study_hours         4     864.0 89211 3055.0
## + gender:wkly_study_hours                 2     256.1 89819 3055.0
## + parent_marital_status:transport_means   3     532.3 89542 3055.2
## + parent_educ:practice_sport             10    2607.2 87468 3055.3
## + parent_educ:parent_marital_status      15    4009.3 86065 3055.8
## + is_first_child:wkly_study_hours         2     126.1 89949 3055.8
## - ethnic_group:transport_means            4    1728.8 91804 3055.9
## + transport_means:wkly_study_hours        2     113.9 89961 3055.9
## + practice_sport:transport_means          2     112.5 89962 3055.9
## - lunch_type:wkly_study_hours             2    1152.6 91227 3056.2
## + test_prep:parent_marital_status         3     350.7 89724 3056.4
## + parent_educ:is_first_child              5     948.3 89126 3056.4
## - lunch_type:practice_sport               2    1201.6 91276 3056.5
## + practice_sport:is_first_child           2      20.0 90055 3056.6
## + ethnic_group:lunch_type                 4     607.8 89467 3056.7
## + ethnic_group:test_prep                  4     594.8 89480 3056.8
## + gender:ethnic_group                     4     554.4 89520 3057.0
## + ethnic_group:parent_marital_status     11    2638.8 87436 3057.1
## + gender:parent_marital_status            3     203.9 89871 3057.3
## + lunch_type:parent_marital_status        3     174.4 89900 3057.5
## - parent_marital_status:wkly_study_hours  6    2636.8 92712 3057.7
## + ethnic_group:is_first_child             4     345.1 89730 3058.4
## + parent_educ:wkly_study_hours           10    2142.9 87932 3058.5
## + parent_educ:transport_means             5     600.4 89474 3058.7
## + gender:parent_educ                      5     465.6 89609 3059.6
## + ethnic_group:practice_sport             8    1357.1 88718 3059.7
## + parent_marital_status:practice_sport    6     716.6 89358 3060.0
## - parent_marital_status:is_first_child    3    2113.0 92188 3060.4
## + parent_educ:lunch_type                  5     343.3 89731 3060.4
## + parent_educ:test_prep                   5     264.1 89811 3060.9
## + ethnic_group:wkly_study_hours           8     452.4 89622 3065.7
## + ethnic_group:parent_educ               20    2115.9 87959 3078.7
## - parent_educ                             5    6269.5 96344 3082.4
## 
## Step:  AIC=3052.12
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:transport_means              1     262.4 90863 3051.8
## <none>                                                90601 3052.1
## - test_prep:transport_means               1     326.9 90928 3052.2
## + gender:practice_sport                   2     526.0 90075 3052.7
## + gender:is_first_child                   1     218.3 90382 3052.7
## + lunch_type:is_first_child               1     150.8 90450 3053.1
## + is_first_child:transport_means          1      90.8 90510 3053.5
## + lunch_type:test_prep                    1      63.7 90537 3053.7
## + gender:test_prep                        1      21.3 90579 3054.0
## + test_prep:practice_sport                2     327.6 90273 3054.0
## + practice_sport:wkly_study_hours         4     930.4 89670 3054.0
## + gender:transport_means                  1       8.0 90593 3054.1
## + test_prep:is_first_child                1       7.2 90594 3054.1
## + gender:lunch_type                       1       2.4 90598 3054.1
## + test_prep:wkly_study_hours              2     303.1 90298 3054.1
## + gender:wkly_study_hours                 2     298.6 90302 3054.2
## + parent_marital_status:transport_means   3     501.6 90099 3054.8
## + parent_educ:parent_marital_status      15    4059.5 86541 3055.1
## + transport_means:wkly_study_hours        2     140.5 90460 3055.2
## + is_first_child:wkly_study_hours         2     130.1 90471 3055.3
## - ethnic_group:transport_means            4    1762.1 92363 3055.5
## + practice_sport:transport_means          2      85.4 90515 3055.6
## - lunch_type:wkly_study_hours             2    1156.5 91757 3055.6
## + parent_educ:is_first_child              5     955.4 89645 3055.9
## + ethnic_group:parent_marital_status     11    2757.1 87844 3055.9
## + test_prep:parent_marital_status         3     340.6 90260 3055.9
## + practice_sport:is_first_child           2      14.2 90587 3056.0
## - lunch_type:practice_sport               2    1234.5 91835 3056.1
## + ethnic_group:test_prep                  4     608.3 89992 3056.1
## + parent_educ:practice_sport             10    2370.5 88230 3056.5
## + ethnic_group:lunch_type                 4     550.1 90051 3056.5
## - parent_marital_status:wkly_study_hours  6    2560.9 93162 3056.6
## + gender:ethnic_group                     4     526.6 90074 3056.7
## + gender:parent_marital_status            3     213.9 90387 3056.7
## + lunch_type:parent_marital_status        3     164.7 90436 3057.0
## + ethnic_group:is_first_child             4     357.4 90243 3057.8
## + parent_educ:transport_means             5     589.9 90011 3058.3
## + ethnic_group:practice_sport             8    1489.7 89111 3058.3
## + parent_educ:wkly_study_hours           10    2057.4 88543 3058.6
## + gender:parent_educ                      5     482.3 90118 3059.0
## - parent_marital_status:is_first_child    3    2053.4 92654 3059.3
## + parent_marital_status:practice_sport    6     723.2 89878 3059.4
## + parent_educ:lunch_type                  5     389.3 90212 3059.6
## + parent_educ:test_prep                   5     259.3 90341 3060.4
## + ethnic_group:wkly_study_hours           8     436.2 90165 3065.3
## + ethnic_group:parent_educ               20    2189.7 88411 3077.7
## - parent_educ                             5    6278.7 96879 3081.7
## - gender                                  1    8889.6 99490 3105.3
## 
## Step:  AIC=3051.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     test_prep:transport_means + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:transport_means               1     300.1 91163 3051.8
## <none>                                                90863 3051.8
## + lunch_type:transport_means              1     262.4 90601 3052.1
## + gender:is_first_child                   1     254.3 90609 3052.2
## + gender:practice_sport                   2     545.1 90318 3052.3
## + lunch_type:is_first_child               1     138.9 90724 3052.9
## + is_first_child:transport_means          1      89.3 90774 3053.2
## + lunch_type:test_prep                    1      40.2 90823 3053.6
## + gender:test_prep                        1      27.3 90836 3053.6
## + test_prep:is_first_child                1      16.5 90847 3053.7
## + gender:transport_means                  1      13.3 90850 3053.7
## + test_prep:practice_sport                2     311.6 90551 3053.8
## + gender:lunch_type                       1       0.7 90862 3053.8
## + gender:wkly_study_hours                 2     303.7 90559 3053.8
## + practice_sport:wkly_study_hours         4     876.1 89987 3054.1
## + test_prep:wkly_study_hours              2     231.4 90632 3054.3
## + parent_marital_status:transport_means   3     501.6 90362 3054.6
## + parent_educ:parent_marital_status      15    4074.5 86789 3054.8
## + transport_means:wkly_study_hours        2     135.8 90727 3054.9
## + is_first_child:wkly_study_hours         2     130.2 90733 3055.0
## - ethnic_group:transport_means            4    1751.0 92614 3055.1
## - lunch_type:wkly_study_hours             2    1125.4 91989 3055.1
## + practice_sport:transport_means          2      93.8 90769 3055.2
## - lunch_type:practice_sport               2    1176.8 92040 3055.4
## + test_prep:parent_marital_status         3     352.3 90511 3055.5
## + ethnic_group:parent_marital_status     11    2754.8 88108 3055.7
## + practice_sport:is_first_child           2      18.0 90845 3055.7
## + parent_educ:is_first_child              5     919.1 89944 3055.8
## + ethnic_group:test_prep                  4     595.6 90267 3055.9
## + ethnic_group:lunch_type                 4     591.5 90272 3056.0
## + gender:parent_marital_status            3     236.6 90627 3056.3
## - parent_marital_status:wkly_study_hours  6    2586.1 93449 3056.4
## + parent_educ:practice_sport             10    2339.6 88524 3056.4
## + gender:ethnic_group                     4     509.1 90354 3056.5
## + lunch_type:parent_marital_status        3     183.6 90680 3056.6
## + ethnic_group:is_first_child             4     324.0 90539 3057.7
## + parent_educ:transport_means             5     598.1 90265 3057.9
## + gender:parent_educ                      5     547.4 90316 3058.3
## + parent_educ:wkly_study_hours           10    2035.7 88827 3058.4
## + ethnic_group:practice_sport             8    1397.2 89466 3058.7
## + parent_marital_status:practice_sport    6     746.8 90116 3058.9
## - parent_marital_status:is_first_child    3    2062.9 92926 3059.1
## + parent_educ:lunch_type                  5     398.6 90465 3059.2
## + parent_educ:test_prep                   5     285.8 90577 3060.0
## + ethnic_group:wkly_study_hours           8     399.8 90463 3065.2
## + ethnic_group:parent_educ               20    2151.2 88712 3077.7
## - parent_educ                             5    6148.1 97011 3080.4
## - gender                                  1    8826.3 99689 3104.5
## 
## Step:  AIC=3051.77
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## <none>                                                91163 3051.8
## + test_prep:transport_means               1     300.1 90863 3051.8
## + gender:is_first_child                   1     257.6 90906 3052.1
## + lunch_type:transport_means              1     235.6 90928 3052.2
## + gender:practice_sport                   2     530.8 90632 3052.3
## + lunch_type:is_first_child               1     114.5 91049 3053.0
## + is_first_child:transport_means          1     108.6 91055 3053.1
## + lunch_type:test_prep                    1      42.2 91121 3053.5
## + gender:transport_means                  1      24.2 91139 3053.6
## + gender:test_prep                        1      23.3 91140 3053.6
## + test_prep:is_first_child                1      18.2 91145 3053.7
## + test_prep:practice_sport                2     325.8 90837 3053.7
## + gender:wkly_study_hours                 2     322.6 90841 3053.7
## + gender:lunch_type                       1       0.0 91163 3053.8
## + practice_sport:wkly_study_hours         4     872.4 90291 3054.1
## + parent_educ:parent_marital_status      15    4174.7 86989 3054.1
## - lunch_type:wkly_study_hours             2     997.2 92160 3054.2
## + parent_marital_status:transport_means   3     537.0 90626 3054.3
## + test_prep:wkly_study_hours              2     211.0 90952 3054.4
## + is_first_child:wkly_study_hours         2     140.3 91023 3054.9
## + transport_means:wkly_study_hours        2     101.6 91062 3055.1
## + practice_sport:transport_means          2      92.2 91071 3055.2
## + test_prep:parent_marital_status         3     391.9 90771 3055.2
## - lunch_type:practice_sport               2    1208.9 92372 3055.5
## + parent_educ:is_first_child              5     948.5 90215 3055.6
## + ethnic_group:parent_marital_status     11    2759.5 88404 3055.6
## + practice_sport:is_first_child           2      16.4 91147 3055.7
## + ethnic_group:lunch_type                 4     617.0 90546 3055.8
## - ethnic_group:transport_means            4    1874.3 93037 3055.8
## - parent_marital_status:wkly_study_hours  6    2516.2 93679 3055.8
## + ethnic_group:test_prep                  4     578.0 90585 3056.0
## + gender:parent_marital_status            3     248.6 90915 3056.2
## + parent_educ:practice_sport             10    2364.5 88799 3056.3
## + gender:ethnic_group                     4     528.5 90635 3056.3
## + lunch_type:parent_marital_status        3     187.1 90976 3056.6
## + ethnic_group:is_first_child             4     297.7 90866 3057.8
## + parent_educ:transport_means             5     601.1 90562 3057.9
## + gender:parent_educ                      5     541.0 90622 3058.3
## + ethnic_group:practice_sport             8    1451.3 89712 3058.3
## + parent_educ:wkly_study_hours           10    2050.0 89113 3058.3
## + parent_marital_status:practice_sport    6     769.8 90393 3058.8
## + parent_educ:lunch_type                  5     420.7 90743 3059.0
## - parent_marital_status:is_first_child    3    2087.3 93251 3059.1
## + parent_educ:test_prep                   5     312.8 90850 3059.7
## + ethnic_group:wkly_study_hours           8     406.7 90757 3065.1
## + ethnic_group:parent_educ               20    2088.9 89074 3078.1
## - test_prep                               1    4865.5 96029 3080.4
## - parent_educ                             5    6366.3 97530 3081.6
## - gender                                  1    8627.7 99791 3103.1
summary(stepwise_model_read)
## 
## Call:
## lm(formula = reading_score ~ gender + ethnic_group + parent_educ + 
##     lunch_type + test_prep + parent_marital_status + practice_sport + 
##     is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, 
##     data = df_4_mdl_read)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -44.540  -8.273  -0.267   9.481  33.728 
## 
## Coefficients:
##                                                     Estimate Std. Error t value
## (Intercept)                                          64.0126     5.6402  11.349
## gendermale                                           -7.9731     1.1041  -7.221
## ethnic_groupgroup B                                   4.0052     3.7361   1.072
## ethnic_groupgroup C                                   4.5817     3.4195   1.340
## ethnic_groupgroup D                                   4.6170     3.5000   1.319
## ethnic_groupgroup E                                  13.9574     3.8663   3.610
## parent_educbachelor's degree                          3.3736     1.9408   1.738
## parent_educhigh school                               -5.9247     1.6817  -3.523
## parent_educmaster's degree                            3.4397     2.4234   1.419
## parent_educsome college                              -2.3224     1.6870  -1.377
## parent_educsome high school                          -5.3232     1.6969  -3.137
## lunch_typestandard                                    2.0599     3.8020   0.542
## test_prepnone                                        -6.2162     1.1463  -5.423
## parent_marital_statusmarried                         10.2557     4.0650   2.523
## parent_marital_statussingle                          -0.8882     4.4420  -0.200
## parent_marital_statuswidowed                         17.2457    10.8292   1.593
## practice_sportregularly                              -4.4245     3.2294  -1.370
## practice_sportsometimes                              -5.4217     3.1279  -1.733
## is_first_childyes                                     8.8087     3.3685   2.615
## transport_meansschool_bus                             7.1540     3.8499   1.858
## wkly_study_hours> 10                                -15.1280     5.0552  -2.993
## wkly_study_hours10-May                                1.2358     3.6575   0.338
## ethnic_groupgroup B:transport_meansschool_bus        -8.5078     4.6456  -1.831
## ethnic_groupgroup C:transport_meansschool_bus        -8.7787     4.3480  -2.019
## ethnic_groupgroup D:transport_meansschool_bus        -2.4914     4.4269  -0.563
## ethnic_groupgroup E:transport_meansschool_bus       -12.1513     4.8881  -2.486
## lunch_typestandard:practice_sportregularly            4.3134     3.9100   1.103
## lunch_typestandard:practice_sportsometimes            9.0693     3.8110   2.380
## lunch_typestandard:wkly_study_hours> 10               6.1827     3.4568   1.789
## lunch_typestandard:wkly_study_hours10-May            -1.3341     2.6912  -0.496
## parent_marital_statusmarried:is_first_childyes      -10.3012     3.6911  -2.791
## parent_marital_statussingle:is_first_childyes        -2.7153     4.1037  -0.662
## parent_marital_statuswidowed:is_first_childyes      -11.5351     8.6888  -1.328
## parent_marital_statusmarried:wkly_study_hours> 10    11.8333     4.9161   2.407
## parent_marital_statussingle:wkly_study_hours> 10     20.4572     5.5006   3.719
## parent_marital_statuswidowed:wkly_study_hours> 10     5.7848    14.3577   0.403
## parent_marital_statusmarried:wkly_study_hours10-May   1.7018     3.6640   0.464
## parent_marital_statussingle:wkly_study_hours10-May    5.0455     4.1368   1.220
## parent_marital_statuswidowed:wkly_study_hours10-May  -3.6043    10.7836  -0.334
##                                                     Pr(>|t|)    
## (Intercept)                                          < 2e-16 ***
## gendermale                                          1.72e-12 ***
## ethnic_groupgroup B                                 0.284174    
## ethnic_groupgroup C                                 0.180841    
## ethnic_groupgroup D                                 0.187673    
## ethnic_groupgroup E                                 0.000334 ***
## parent_educbachelor's degree                        0.082717 .  
## parent_educhigh school                              0.000462 ***
## parent_educmaster's degree                          0.156352    
## parent_educsome college                             0.169188    
## parent_educsome high school                         0.001798 ** 
## lunch_typestandard                                  0.588175    
## test_prepnone                                       8.79e-08 ***
## parent_marital_statusmarried                        0.011918 *  
## parent_marital_statussingle                         0.841585    
## parent_marital_statuswidowed                        0.111840    
## practice_sportregularly                             0.171222    
## practice_sportsometimes                             0.083598 .  
## is_first_childyes                                   0.009167 ** 
## transport_meansschool_bus                           0.063672 .  
## wkly_study_hours> 10                                0.002890 ** 
## wkly_study_hours10-May                              0.735589    
## ethnic_groupgroup B:transport_meansschool_bus       0.067585 .  
## ethnic_groupgroup C:transport_meansschool_bus       0.043967 *  
## ethnic_groupgroup D:transport_meansschool_bus       0.573809    
## ethnic_groupgroup E:transport_meansschool_bus       0.013218 *  
## lunch_typestandard:practice_sportregularly          0.270437    
## lunch_typestandard:practice_sportsometimes          0.017661 *  
## lunch_typestandard:wkly_study_hours> 10             0.074233 .  
## lunch_typestandard:wkly_study_hours10-May           0.620296    
## parent_marital_statusmarried:is_first_childyes      0.005440 ** 
## parent_marital_statussingle:is_first_childyes       0.508448    
## parent_marital_statuswidowed:is_first_childyes      0.184867    
## parent_marital_statusmarried:wkly_study_hours> 10   0.016410 *  
## parent_marital_statussingle:wkly_study_hours> 10    0.000220 ***
## parent_marital_statuswidowed:wkly_study_hours> 10   0.687173    
## parent_marital_statusmarried:wkly_study_hours10-May 0.642503    
## parent_marital_statussingle:wkly_study_hours10-May  0.223116    
## parent_marital_statuswidowed:wkly_study_hours10-May 0.738324    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.86 on 551 degrees of freedom
## Multiple R-squared:  0.3254, Adjusted R-squared:  0.2789 
## F-statistic: 6.995 on 38 and 551 DF,  p-value: < 2.2e-16

Diagnostics

Writing

plot(stepwise_model_write)

step_as_lm_write=lm(formula = writing_score ~ gender + ethnic_group + parent_educ + 
    lunch_type + test_prep + parent_marital_status + practice_sport + 
    is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
    lunch_type:practice_sport + lunch_type:wkly_study_hours + 
    parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, data = df_4_mdl_write)

library('MASS')
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:gtsummary':
## 
##     select
## The following object is masked from 'package:dplyr':
## 
##     select
boxcox(step_as_lm_write)

step_as_lm_write=lm(formula = (writing_score)^2 ~ gender + ethnic_group + parent_educ + 
    lunch_type + test_prep + parent_marital_status + practice_sport + 
    is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
    lunch_type:practice_sport + lunch_type:wkly_study_hours + 
    parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, data = df_4_mdl_write)

plot(step_as_lm_write)

plot(stepwise_model_math)
## Warning: not plotting observations with leverage one:
##   190

step_as_lm_math=lm(formula = math_score ~ gender + ethnic_group + parent_educ + 
    lunch_type + test_prep + parent_marital_status + practice_sport + 
    is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
    parent_educ:parent_marital_status + parent_educ:is_first_child + 
    lunch_type:practice_sport + lunch_type:transport_means + 
    test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
    parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
    is_first_child:transport_means + is_first_child:wkly_study_hours,data = df_4_mdl_math)
plot(stepwise_model_read)

##ADD in other scores

Writing Score2

df_4_mdl_write2=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,writing_score,math_score,reading_score)
full_fit_write2=lm(writing_score ~ .^2,data=df_4_mdl_write2)
summary(full_fit_write2)
## 
## Call:
## lm(formula = writing_score ~ .^2, data = df_4_mdl_write2)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -6.997 -1.687  0.000  1.784  7.682 
## 
## Coefficients: (6 not defined because of singularities)
##                                                             Estimate Std. Error
## (Intercept)                                                1.028e+01  8.576e+00
## gendermale                                                -7.013e+00  3.989e+00
## ethnic_groupgroup B                                        3.669e-01  6.023e+00
## ethnic_groupgroup C                                       -3.800e+00  5.577e+00
## ethnic_groupgroup D                                        3.108e+00  5.859e+00
## ethnic_groupgroup E                                        3.619e+00  5.900e+00
## parent_educbachelor's degree                              -2.540e+00  5.912e+00
## parent_educhigh school                                     7.053e-01  4.353e+00
## parent_educmaster's degree                                 1.423e+01  6.930e+00
## parent_educsome college                                   -3.972e+00  4.298e+00
## parent_educsome high school                                9.619e-01  4.179e+00
## lunch_typestandard                                         1.690e+00  3.496e+00
## test_prepnone                                             -3.741e+00  3.414e+00
## parent_marital_statusmarried                               7.848e+00  4.378e+00
## parent_marital_statussingle                                9.743e+00  5.012e+00
## parent_marital_statuswidowed                               2.301e+00  1.116e+01
## practice_sportregularly                                   -6.078e+00  5.488e+00
## practice_sportsometimes                                   -8.824e+00  5.349e+00
## is_first_childyes                                         -1.382e+00  3.323e+00
## transport_meansschool_bus                                 -6.443e+00  3.169e+00
## wkly_study_hours> 10                                       1.226e+00  4.722e+00
## wkly_study_hours10-May                                    -2.133e+00  3.735e+00
## math_score                                                 2.128e-01  2.386e-01
## reading_score                                              7.610e-01  2.255e-01
## gendermale:ethnic_groupgroup B                            -4.528e+00  2.318e+00
## gendermale:ethnic_groupgroup C                            -3.411e+00  2.215e+00
## gendermale:ethnic_groupgroup D                            -2.747e+00  2.176e+00
## gendermale:ethnic_groupgroup E                            -4.336e+00  2.470e+00
## gendermale:parent_educbachelor's degree                    1.915e+00  1.709e+00
## gendermale:parent_educhigh school                          8.177e-01  1.419e+00
## gendermale:parent_educmaster's degree                     -1.360e-01  3.810e+00
## gendermale:parent_educsome college                         1.738e-01  1.488e+00
## gendermale:parent_educsome high school                    -3.763e-01  1.495e+00
## gendermale:lunch_typestandard                             -1.093e-01  1.143e+00
## gendermale:test_prepnone                                   3.385e-01  1.108e+00
## gendermale:parent_marital_statusmarried                   -2.482e-01  1.519e+00
## gendermale:parent_marital_statussingle                     1.505e+00  1.728e+00
## gendermale:parent_marital_statuswidowed                    4.344e-01  4.909e+00
## gendermale:practice_sportregularly                         5.286e-01  2.043e+00
## gendermale:practice_sportsometimes                         3.329e-01  1.971e+00
## gendermale:is_first_childyes                               1.137e+00  1.132e+00
## gendermale:transport_meansschool_bus                       3.868e-01  1.002e+00
## gendermale:wkly_study_hours> 10                           -1.949e+00  1.673e+00
## gendermale:wkly_study_hours10-May                         -9.213e-01  1.184e+00
## gendermale:math_score                                     -4.901e-02  5.875e-02
## gendermale:reading_score                                   8.724e-02  6.041e-02
## ethnic_groupgroup B:parent_educbachelor's degree          -2.360e+00  3.631e+00
## ethnic_groupgroup C:parent_educbachelor's degree          -3.922e+00  3.587e+00
## ethnic_groupgroup D:parent_educbachelor's degree          -4.107e+00  3.539e+00
## ethnic_groupgroup E:parent_educbachelor's degree          -2.158e+00  4.239e+00
## ethnic_groupgroup B:parent_educhigh school                -2.294e+00  2.179e+00
## ethnic_groupgroup C:parent_educhigh school                -2.333e+00  2.069e+00
## ethnic_groupgroup D:parent_educhigh school                -1.623e+00  2.103e+00
## ethnic_groupgroup E:parent_educhigh school                -3.068e+00  2.385e+00
## ethnic_groupgroup B:parent_educmaster's degree            -1.163e+01  4.440e+00
## ethnic_groupgroup C:parent_educmaster's degree            -1.099e+01  3.994e+00
## ethnic_groupgroup D:parent_educmaster's degree            -8.580e+00  4.058e+00
## ethnic_groupgroup E:parent_educmaster's degree            -8.886e+00  4.384e+00
## ethnic_groupgroup B:parent_educsome college               -1.154e+00  2.454e+00
## ethnic_groupgroup C:parent_educsome college               -8.806e-01  2.278e+00
## ethnic_groupgroup D:parent_educsome college               -2.386e+00  2.390e+00
## ethnic_groupgroup E:parent_educsome college               -4.769e+00  2.430e+00
## ethnic_groupgroup B:parent_educsome high school           -4.318e+00  2.358e+00
## ethnic_groupgroup C:parent_educsome high school           -4.749e+00  2.163e+00
## ethnic_groupgroup D:parent_educsome high school           -3.744e+00  2.166e+00
## ethnic_groupgroup E:parent_educsome high school           -7.797e+00  2.355e+00
## ethnic_groupgroup B:lunch_typestandard                    -4.576e+00  1.727e+00
## ethnic_groupgroup C:lunch_typestandard                    -4.132e+00  1.672e+00
## ethnic_groupgroup D:lunch_typestandard                    -5.504e+00  1.637e+00
## ethnic_groupgroup E:lunch_typestandard                    -3.755e+00  1.976e+00
## ethnic_groupgroup B:test_prepnone                          7.983e-02  1.730e+00
## ethnic_groupgroup C:test_prepnone                         -8.576e-01  1.616e+00
## ethnic_groupgroup D:test_prepnone                         -1.329e+00  1.612e+00
## ethnic_groupgroup E:test_prepnone                         -6.585e-01  1.755e+00
## ethnic_groupgroup B:parent_marital_statusmarried          -4.694e+00  2.252e+00
## ethnic_groupgroup C:parent_marital_statusmarried          -3.813e+00  1.992e+00
## ethnic_groupgroup D:parent_marital_statusmarried          -3.013e+00  1.991e+00
## ethnic_groupgroup E:parent_marital_statusmarried          -4.379e+00  2.264e+00
## ethnic_groupgroup B:parent_marital_statussingle           -6.236e+00  2.612e+00
## ethnic_groupgroup C:parent_marital_statussingle           -4.982e+00  2.421e+00
## ethnic_groupgroup D:parent_marital_statussingle           -4.474e+00  2.384e+00
## ethnic_groupgroup E:parent_marital_statussingle           -8.456e+00  2.778e+00
## ethnic_groupgroup B:parent_marital_statuswidowed           4.573e+00  2.910e+01
## ethnic_groupgroup C:parent_marital_statuswidowed           1.408e+01  2.461e+01
## ethnic_groupgroup D:parent_marital_statuswidowed           6.284e-01  2.303e+01
## ethnic_groupgroup E:parent_marital_statuswidowed                  NA         NA
## ethnic_groupgroup B:practice_sportregularly                2.264e+00  2.949e+00
## ethnic_groupgroup C:practice_sportregularly                4.746e+00  2.905e+00
## ethnic_groupgroup D:practice_sportregularly                1.567e+00  3.190e+00
## ethnic_groupgroup E:practice_sportregularly               -1.058e+00  3.052e+00
## ethnic_groupgroup B:practice_sportsometimes                2.424e+00  3.132e+00
## ethnic_groupgroup C:practice_sportsometimes                4.488e+00  3.023e+00
## ethnic_groupgroup D:practice_sportsometimes                2.401e+00  3.280e+00
## ethnic_groupgroup E:practice_sportsometimes                1.404e+00  3.099e+00
## ethnic_groupgroup B:is_first_childyes                      2.061e+00  1.583e+00
## ethnic_groupgroup C:is_first_childyes                      3.185e+00  1.484e+00
## ethnic_groupgroup D:is_first_childyes                      2.468e+00  1.515e+00
## ethnic_groupgroup E:is_first_childyes                      3.012e+00  1.753e+00
## ethnic_groupgroup B:transport_meansschool_bus             -1.396e-01  1.638e+00
## ethnic_groupgroup C:transport_meansschool_bus             -7.759e-02  1.498e+00
## ethnic_groupgroup D:transport_meansschool_bus             -1.696e+00  1.497e+00
## ethnic_groupgroup E:transport_meansschool_bus             -1.491e+00  1.825e+00
## ethnic_groupgroup B:wkly_study_hours> 10                   5.802e-01  2.726e+00
## ethnic_groupgroup C:wkly_study_hours> 10                   1.954e-01  2.722e+00
## ethnic_groupgroup D:wkly_study_hours> 10                   3.977e+00  2.734e+00
## ethnic_groupgroup E:wkly_study_hours> 10                   1.303e+00  2.947e+00
## ethnic_groupgroup B:wkly_study_hours10-May                -2.546e-01  2.236e+00
## ethnic_groupgroup C:wkly_study_hours10-May                 1.636e+00  2.192e+00
## ethnic_groupgroup D:wkly_study_hours10-May                 2.822e+00  2.233e+00
## ethnic_groupgroup E:wkly_study_hours10-May                 3.406e+00  2.445e+00
## ethnic_groupgroup B:math_score                             3.236e-01  1.452e-01
## ethnic_groupgroup C:math_score                             2.304e-01  1.365e-01
## ethnic_groupgroup D:math_score                             2.338e-01  1.351e-01
## ethnic_groupgroup E:math_score                             2.302e-01  1.600e-01
## ethnic_groupgroup B:reading_score                         -1.914e-01  1.362e-01
## ethnic_groupgroup C:reading_score                         -1.056e-01  1.296e-01
## ethnic_groupgroup D:reading_score                         -1.470e-01  1.272e-01
## ethnic_groupgroup E:reading_score                         -1.390e-01  1.506e-01
## parent_educbachelor's degree:lunch_typestandard            9.535e-01  1.525e+00
## parent_educhigh school:lunch_typestandard                  9.227e-01  1.205e+00
## parent_educmaster's degree:lunch_typestandard             -8.538e-01  3.193e+00
## parent_educsome college:lunch_typestandard                 2.284e+00  1.225e+00
## parent_educsome high school:lunch_typestandard            -1.360e-01  1.292e+00
## parent_educbachelor's degree:test_prepnone                 1.560e+00  1.290e+00
## parent_educhigh school:test_prepnone                       9.003e-01  1.230e+00
## parent_educmaster's degree:test_prepnone                  -3.015e+00  2.150e+00
## parent_educsome college:test_prepnone                      1.179e+00  1.144e+00
## parent_educsome high school:test_prepnone                 -5.264e-02  1.115e+00
## parent_educbachelor's degree:parent_marital_statusmarried -8.048e-01  2.433e+00
## parent_educhigh school:parent_marital_statusmarried       -1.460e+00  1.679e+00
## parent_educmaster's degree:parent_marital_statusmarried    4.700e+00  2.454e+00
## parent_educsome college:parent_marital_statusmarried       1.767e+00  1.575e+00
## parent_educsome high school:parent_marital_statusmarried   9.859e-01  1.551e+00
## parent_educbachelor's degree:parent_marital_statussingle  -1.603e+00  2.721e+00
## parent_educhigh school:parent_marital_statussingle        -1.213e-02  1.797e+00
## parent_educmaster's degree:parent_marital_statussingle     2.822e+00  2.512e+00
## parent_educsome college:parent_marital_statussingle        1.659e+00  1.731e+00
## parent_educsome high school:parent_marital_statussingle   -4.275e-01  1.752e+00
## parent_educbachelor's degree:parent_marital_statuswidowed  5.047e+00  2.313e+01
## parent_educhigh school:parent_marital_statuswidowed        2.332e+00  2.647e+01
## parent_educmaster's degree:parent_marital_statuswidowed   -7.201e+00  1.459e+01
## parent_educsome college:parent_marital_statuswidowed      -8.571e+00  1.816e+01
## parent_educsome high school:parent_marital_statuswidowed  -5.909e+00  2.125e+01
## parent_educbachelor's degree:practice_sportregularly       5.133e+00  2.376e+00
## parent_educhigh school:practice_sportregularly             2.626e+00  1.959e+00
## parent_educmaster's degree:practice_sportregularly         5.789e-01  2.823e+00
## parent_educsome college:practice_sportregularly            5.130e-01  1.989e+00
## parent_educsome high school:practice_sportregularly        4.815e-01  1.910e+00
## parent_educbachelor's degree:practice_sportsometimes       3.054e+00  2.271e+00
## parent_educhigh school:practice_sportsometimes             1.137e+00  1.884e+00
## parent_educmaster's degree:practice_sportsometimes        -6.126e-01  2.565e+00
## parent_educsome college:practice_sportsometimes            1.530e+00  1.958e+00
## parent_educsome high school:practice_sportsometimes       -2.079e+00  1.792e+00
## parent_educbachelor's degree:is_first_childyes             2.548e+00  1.357e+00
## parent_educhigh school:is_first_childyes                   9.976e-01  1.182e+00
## parent_educmaster's degree:is_first_childyes              -3.160e+00  2.129e+00
## parent_educsome college:is_first_childyes                  2.851e+00  1.161e+00
## parent_educsome high school:is_first_childyes              2.358e+00  1.164e+00
## parent_educbachelor's degree:transport_meansschool_bus     4.026e-01  1.388e+00
## parent_educhigh school:transport_meansschool_bus           7.477e-01  1.102e+00
## parent_educmaster's degree:transport_meansschool_bus       6.615e-01  1.827e+00
## parent_educsome college:transport_meansschool_bus         -8.132e-01  1.128e+00
## parent_educsome high school:transport_meansschool_bus      1.680e+00  1.166e+00
## parent_educbachelor's degree:wkly_study_hours> 10         -1.506e-01  2.039e+00
## parent_educhigh school:wkly_study_hours> 10               -2.687e-01  1.679e+00
## parent_educmaster's degree:wkly_study_hours> 10           -2.737e+00  4.402e+00
## parent_educsome college:wkly_study_hours> 10              -2.302e+00  1.720e+00
## parent_educsome high school:wkly_study_hours> 10          -1.359e+00  1.743e+00
## parent_educbachelor's degree:wkly_study_hours10-May       -7.253e-01  1.418e+00
## parent_educhigh school:wkly_study_hours10-May             -1.045e+00  1.332e+00
## parent_educmaster's degree:wkly_study_hours10-May         -2.224e+00  2.130e+00
## parent_educsome college:wkly_study_hours10-May            -2.599e+00  1.353e+00
## parent_educsome high school:wkly_study_hours10-May        -4.571e-01  1.421e+00
## parent_educbachelor's degree:math_score                   -1.932e-01  1.072e-01
## parent_educhigh school:math_score                         -7.404e-02  8.469e-02
## parent_educmaster's degree:math_score                      1.057e-01  2.392e-01
## parent_educsome college:math_score                         5.119e-03  8.827e-02
## parent_educsome high school:math_score                    -3.364e-02  8.807e-02
## parent_educbachelor's degree:reading_score                 1.891e-01  1.148e-01
## parent_educhigh school:reading_score                       3.758e-02  8.697e-02
## parent_educmaster's degree:reading_score                  -9.233e-02  2.097e-01
## parent_educsome college:reading_score                      2.167e-02  9.021e-02
## parent_educsome high school:reading_score                  3.768e-02  8.729e-02
## lunch_typestandard:test_prepnone                           2.260e-01  9.141e-01
## lunch_typestandard:parent_marital_statusmarried           -3.873e-01  1.196e+00
## lunch_typestandard:parent_marital_statussingle            -1.706e+00  1.393e+00
## lunch_typestandard:parent_marital_statuswidowed            1.749e+00  2.137e+01
## lunch_typestandard:practice_sportregularly                 6.608e-01  1.503e+00
## lunch_typestandard:practice_sportsometimes                 1.637e+00  1.411e+00
## lunch_typestandard:is_first_childyes                      -9.874e-01  9.280e-01
## lunch_typestandard:transport_meansschool_bus              -1.920e-01  8.672e-01
## lunch_typestandard:wkly_study_hours> 10                   -3.781e-01  1.331e+00
## lunch_typestandard:wkly_study_hours10-May                  3.552e-01  1.014e+00
## lunch_typestandard:math_score                              3.561e-02  6.063e-02
## lunch_typestandard:reading_score                          -4.639e-03  6.218e-02
## test_prepnone:parent_marital_statusmarried                -3.030e+00  1.151e+00
## test_prepnone:parent_marital_statussingle                 -2.900e+00  1.329e+00
## test_prepnone:parent_marital_statuswidowed                -8.578e+00  1.207e+01
## test_prepnone:practice_sportregularly                      3.008e-01  1.444e+00
## test_prepnone:practice_sportsometimes                      1.806e+00  1.406e+00
## test_prepnone:is_first_childyes                           -9.820e-01  8.431e-01
## test_prepnone:transport_meansschool_bus                    1.484e+00  7.799e-01
## test_prepnone:wkly_study_hours> 10                         1.023e-01  1.199e+00
## test_prepnone:wkly_study_hours10-May                       5.061e-01  9.656e-01
## test_prepnone:math_score                                  -8.815e-03  6.136e-02
## test_prepnone:reading_score                                2.202e-02  6.343e-02
## parent_marital_statusmarried:practice_sportregularly      -1.129e+00  1.761e+00
## parent_marital_statussingle:practice_sportregularly       -2.999e+00  2.393e+00
## parent_marital_statuswidowed:practice_sportregularly      -6.007e+00  2.241e+01
## parent_marital_statusmarried:practice_sportsometimes      -3.916e-01  1.754e+00
## parent_marital_statussingle:practice_sportsometimes       -2.731e+00  2.338e+00
## parent_marital_statuswidowed:practice_sportsometimes              NA         NA
## parent_marital_statusmarried:is_first_childyes            -4.629e-01  1.419e+00
## parent_marital_statussingle:is_first_childyes             -4.861e-01  1.526e+00
## parent_marital_statuswidowed:is_first_childyes             6.577e+00  8.406e+00
## parent_marital_statusmarried:transport_meansschool_bus    -4.278e-01  1.115e+00
## parent_marital_statussingle:transport_meansschool_bus      9.514e-01  1.272e+00
## parent_marital_statuswidowed:transport_meansschool_bus    -2.336e+00  5.656e+00
## parent_marital_statusmarried:wkly_study_hours> 10          1.170e-01  1.870e+00
## parent_marital_statussingle:wkly_study_hours> 10           1.130e+00  2.047e+00
## parent_marital_statuswidowed:wkly_study_hours> 10                 NA         NA
## parent_marital_statusmarried:wkly_study_hours10-May        2.756e+00  1.205e+00
## parent_marital_statussingle:wkly_study_hours10-May         3.963e+00  1.348e+00
## parent_marital_statuswidowed:wkly_study_hours10-May               NA         NA
## parent_marital_statusmarried:math_score                    2.480e-02  9.188e-02
## parent_marital_statussingle:math_score                    -7.269e-02  1.017e-01
## parent_marital_statuswidowed:math_score                           NA         NA
## parent_marital_statusmarried:reading_score                -6.129e-02  9.651e-02
## parent_marital_statussingle:reading_score                  3.787e-02  1.069e-01
## parent_marital_statuswidowed:reading_score                        NA         NA
## practice_sportregularly:is_first_childyes                 -2.264e+00  1.585e+00
## practice_sportsometimes:is_first_childyes                 -1.184e+00  1.538e+00
## practice_sportregularly:transport_meansschool_bus          1.020e+00  1.371e+00
## practice_sportsometimes:transport_meansschool_bus          7.856e-01  1.330e+00
## practice_sportregularly:wkly_study_hours> 10               1.816e+00  1.893e+00
## practice_sportsometimes:wkly_study_hours> 10               3.907e-01  1.870e+00
## practice_sportregularly:wkly_study_hours10-May            -4.035e-02  1.453e+00
## practice_sportsometimes:wkly_study_hours10-May            -8.301e-01  1.430e+00
## practice_sportregularly:math_score                         4.761e-02  1.358e-01
## practice_sportsometimes:math_score                         7.168e-03  1.328e-01
## practice_sportregularly:reading_score                      2.189e-02  1.325e-01
## practice_sportsometimes:reading_score                      6.724e-02  1.290e-01
## is_first_childyes:transport_meansschool_bus               -4.867e-01  8.253e-01
## is_first_childyes:wkly_study_hours> 10                     1.378e+00  1.219e+00
## is_first_childyes:wkly_study_hours10-May                   1.474e+00  9.252e-01
## is_first_childyes:math_score                              -6.407e-02  6.526e-02
## is_first_childyes:reading_score                            4.464e-02  6.619e-02
## transport_meansschool_bus:wkly_study_hours> 10            -7.931e-02  1.197e+00
## transport_meansschool_bus:wkly_study_hours10-May          -8.356e-01  8.378e-01
## transport_meansschool_bus:math_score                       3.887e-02  6.030e-02
## transport_meansschool_bus:reading_score                    4.383e-02  6.201e-02
## wkly_study_hours> 10:math_score                            1.049e-01  9.306e-02
## wkly_study_hours10-May:math_score                         -1.912e-03  6.687e-02
## wkly_study_hours> 10:reading_score                        -1.469e-01  9.748e-02
## wkly_study_hours10-May:reading_score                      -1.354e-02  6.492e-02
## math_score:reading_score                                  -1.711e-03  8.452e-04
##                                                           t value Pr(>|t|)    
## (Intercept)                                                 1.199 0.231456    
## gendermale                                                 -1.758 0.079623 .  
## ethnic_groupgroup B                                         0.061 0.951460    
## ethnic_groupgroup C                                        -0.681 0.496075    
## ethnic_groupgroup D                                         0.530 0.596167    
## ethnic_groupgroup E                                         0.613 0.539968    
## parent_educbachelor's degree                               -0.430 0.667787    
## parent_educhigh school                                      0.162 0.871389    
## parent_educmaster's degree                                  2.053 0.040810 *  
## parent_educsome college                                    -0.924 0.356042    
## parent_educsome high school                                 0.230 0.818085    
## lunch_typestandard                                          0.483 0.629192    
## test_prepnone                                              -1.096 0.273983    
## parent_marital_statusmarried                                1.793 0.073914 .  
## parent_marital_statussingle                                 1.944 0.052719 .  
## parent_marital_statuswidowed                                0.206 0.836786    
## practice_sportregularly                                    -1.108 0.268841    
## practice_sportsometimes                                    -1.650 0.099912 .  
## is_first_childyes                                          -0.416 0.677621    
## transport_meansschool_bus                                  -2.033 0.042785 *  
## wkly_study_hours> 10                                        0.260 0.795349    
## wkly_study_hours10-May                                     -0.571 0.568305    
## math_score                                                  0.892 0.373099    
## reading_score                                               3.375 0.000824 ***
## gendermale:ethnic_groupgroup B                             -1.954 0.051551 .  
## gendermale:ethnic_groupgroup C                             -1.540 0.124591    
## gendermale:ethnic_groupgroup D                             -1.262 0.207727    
## gendermale:ethnic_groupgroup E                             -1.756 0.080050 .  
## gendermale:parent_educbachelor's degree                     1.121 0.263118    
## gendermale:parent_educhigh school                           0.576 0.564776    
## gendermale:parent_educmaster's degree                      -0.036 0.971534    
## gendermale:parent_educsome college                          0.117 0.907096    
## gendermale:parent_educsome high school                     -0.252 0.801470    
## gendermale:lunch_typestandard                              -0.096 0.923917    
## gendermale:test_prepnone                                    0.306 0.760096    
## gendermale:parent_marital_statusmarried                    -0.163 0.870316    
## gendermale:parent_marital_statussingle                      0.871 0.384205    
## gendermale:parent_marital_statuswidowed                     0.088 0.929540    
## gendermale:practice_sportregularly                          0.259 0.796023    
## gendermale:practice_sportsometimes                          0.169 0.865950    
## gendermale:is_first_childyes                                1.004 0.315869    
## gendermale:transport_meansschool_bus                        0.386 0.699760    
## gendermale:wkly_study_hours> 10                            -1.165 0.244954    
## gendermale:wkly_study_hours10-May                          -0.778 0.437068    
## gendermale:math_score                                      -0.834 0.404755    
## gendermale:reading_score                                    1.444 0.149600    
## ethnic_groupgroup B:parent_educbachelor's degree           -0.650 0.516141    
## ethnic_groupgroup C:parent_educbachelor's degree           -1.094 0.274921    
## ethnic_groupgroup D:parent_educbachelor's degree           -1.160 0.246726    
## ethnic_groupgroup E:parent_educbachelor's degree           -0.509 0.610969    
## ethnic_groupgroup B:parent_educhigh school                 -1.053 0.293150    
## ethnic_groupgroup C:parent_educhigh school                 -1.128 0.260320    
## ethnic_groupgroup D:parent_educhigh school                 -0.772 0.440647    
## ethnic_groupgroup E:parent_educhigh school                 -1.286 0.199283    
## ethnic_groupgroup B:parent_educmaster's degree             -2.619 0.009201 ** 
## ethnic_groupgroup C:parent_educmaster's degree             -2.750 0.006274 ** 
## ethnic_groupgroup D:parent_educmaster's degree             -2.114 0.035211 *  
## ethnic_groupgroup E:parent_educmaster's degree             -2.027 0.043436 *  
## ethnic_groupgroup B:parent_educsome college                -0.470 0.638494    
## ethnic_groupgroup C:parent_educsome college                -0.387 0.699356    
## ethnic_groupgroup D:parent_educsome college                -0.998 0.318802    
## ethnic_groupgroup E:parent_educsome college                -1.962 0.050544 .  
## ethnic_groupgroup B:parent_educsome high school            -1.831 0.067918 .  
## ethnic_groupgroup C:parent_educsome high school            -2.195 0.028833 *  
## ethnic_groupgroup D:parent_educsome high school            -1.729 0.084730 .  
## ethnic_groupgroup E:parent_educsome high school            -3.311 0.001031 ** 
## ethnic_groupgroup B:lunch_typestandard                     -2.650 0.008431 ** 
## ethnic_groupgroup C:lunch_typestandard                     -2.471 0.013973 *  
## ethnic_groupgroup D:lunch_typestandard                     -3.362 0.000863 ***
## ethnic_groupgroup E:lunch_typestandard                     -1.901 0.058203 .  
## ethnic_groupgroup B:test_prepnone                           0.046 0.963213    
## ethnic_groupgroup C:test_prepnone                          -0.531 0.596082    
## ethnic_groupgroup D:test_prepnone                          -0.825 0.410230    
## ethnic_groupgroup E:test_prepnone                          -0.375 0.707810    
## ethnic_groupgroup B:parent_marital_statusmarried           -2.085 0.037859 *  
## ethnic_groupgroup C:parent_marital_statusmarried           -1.915 0.056384 .  
## ethnic_groupgroup D:parent_marital_statusmarried           -1.513 0.131123    
## ethnic_groupgroup E:parent_marital_statusmarried           -1.935 0.053869 .  
## ethnic_groupgroup B:parent_marital_statussingle            -2.388 0.017499 *  
## ethnic_groupgroup C:parent_marital_statussingle            -2.058 0.040375 *  
## ethnic_groupgroup D:parent_marital_statussingle            -1.876 0.061480 .  
## ethnic_groupgroup E:parent_marital_statussingle            -3.044 0.002519 ** 
## ethnic_groupgroup B:parent_marital_statuswidowed            0.157 0.875232    
## ethnic_groupgroup C:parent_marital_statuswidowed            0.572 0.567578    
## ethnic_groupgroup D:parent_marital_statuswidowed            0.027 0.978245    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                 0.768 0.443133    
## ethnic_groupgroup C:practice_sportregularly                 1.634 0.103284    
## ethnic_groupgroup D:practice_sportregularly                 0.491 0.623729    
## ethnic_groupgroup E:practice_sportregularly                -0.347 0.729127    
## ethnic_groupgroup B:practice_sportsometimes                 0.774 0.439531    
## ethnic_groupgroup C:practice_sportsometimes                 1.484 0.138643    
## ethnic_groupgroup D:practice_sportsometimes                 0.732 0.464661    
## ethnic_groupgroup E:practice_sportsometimes                 0.453 0.650804    
## ethnic_groupgroup B:is_first_childyes                       1.302 0.193881    
## ethnic_groupgroup C:is_first_childyes                       2.146 0.032597 *  
## ethnic_groupgroup D:is_first_childyes                       1.630 0.104116    
## ethnic_groupgroup E:is_first_childyes                       1.718 0.086624 .  
## ethnic_groupgroup B:transport_meansschool_bus              -0.085 0.932158    
## ethnic_groupgroup C:transport_meansschool_bus              -0.052 0.958719    
## ethnic_groupgroup D:transport_meansschool_bus              -1.133 0.258165    
## ethnic_groupgroup E:transport_meansschool_bus              -0.817 0.414538    
## ethnic_groupgroup B:wkly_study_hours> 10                    0.213 0.831564    
## ethnic_groupgroup C:wkly_study_hours> 10                    0.072 0.942813    
## ethnic_groupgroup D:wkly_study_hours> 10                    1.454 0.146733    
## ethnic_groupgroup E:wkly_study_hours> 10                    0.442 0.658552    
## ethnic_groupgroup B:wkly_study_hours10-May                 -0.114 0.909384    
## ethnic_groupgroup C:wkly_study_hours10-May                  0.746 0.456140    
## ethnic_groupgroup D:wkly_study_hours10-May                  1.264 0.207115    
## ethnic_groupgroup E:wkly_study_hours10-May                  1.393 0.164584    
## ethnic_groupgroup B:math_score                              2.228 0.026504 *  
## ethnic_groupgroup C:math_score                              1.688 0.092282 .  
## ethnic_groupgroup D:math_score                              1.730 0.084453 .  
## ethnic_groupgroup E:math_score                              1.439 0.151200    
## ethnic_groupgroup B:reading_score                          -1.406 0.160652    
## ethnic_groupgroup C:reading_score                          -0.815 0.415690    
## ethnic_groupgroup D:reading_score                          -1.156 0.248457    
## ethnic_groupgroup E:reading_score                          -0.922 0.356937    
## parent_educbachelor's degree:lunch_typestandard             0.625 0.532190    
## parent_educhigh school:lunch_typestandard                   0.766 0.444428    
## parent_educmaster's degree:lunch_typestandard              -0.267 0.789339    
## parent_educsome college:lunch_typestandard                  1.864 0.063177 .  
## parent_educsome high school:lunch_typestandard             -0.105 0.916212    
## parent_educbachelor's degree:test_prepnone                  1.209 0.227508    
## parent_educhigh school:test_prepnone                        0.732 0.464686    
## parent_educmaster's degree:test_prepnone                   -1.402 0.161767    
## parent_educsome college:test_prepnone                       1.030 0.303562    
## parent_educsome high school:test_prepnone                  -0.047 0.962354    
## parent_educbachelor's degree:parent_marital_statusmarried  -0.331 0.741044    
## parent_educhigh school:parent_marital_statusmarried        -0.870 0.385073    
## parent_educmaster's degree:parent_marital_statusmarried     1.915 0.056296 .  
## parent_educsome college:parent_marital_statusmarried        1.122 0.262607    
## parent_educsome high school:parent_marital_statusmarried    0.636 0.525383    
## parent_educbachelor's degree:parent_marital_statussingle   -0.589 0.556280    
## parent_educhigh school:parent_marital_statussingle         -0.007 0.994617    
## parent_educmaster's degree:parent_marital_statussingle      1.123 0.262066    
## parent_educsome college:parent_marital_statussingle         0.959 0.338359    
## parent_educsome high school:parent_marital_statussingle    -0.244 0.807365    
## parent_educbachelor's degree:parent_marital_statuswidowed   0.218 0.827400    
## parent_educhigh school:parent_marital_statuswidowed         0.088 0.929870    
## parent_educmaster's degree:parent_marital_statuswidowed    -0.494 0.621922    
## parent_educsome college:parent_marital_statuswidowed       -0.472 0.637175    
## parent_educsome high school:parent_marital_statuswidowed   -0.278 0.781139    
## parent_educbachelor's degree:practice_sportregularly        2.160 0.031468 *  
## parent_educhigh school:practice_sportregularly              1.340 0.181144    
## parent_educmaster's degree:practice_sportregularly          0.205 0.837663    
## parent_educsome college:practice_sportregularly             0.258 0.796631    
## parent_educsome high school:practice_sportregularly         0.252 0.801173    
## parent_educbachelor's degree:practice_sportsometimes        1.345 0.179574    
## parent_educhigh school:practice_sportsometimes              0.604 0.546457    
## parent_educmaster's degree:practice_sportsometimes         -0.239 0.811354    
## parent_educsome college:practice_sportsometimes             0.782 0.434969    
## parent_educsome high school:practice_sportsometimes        -1.160 0.246687    
## parent_educbachelor's degree:is_first_childyes              1.878 0.061283 .  
## parent_educhigh school:is_first_childyes                    0.844 0.399328    
## parent_educmaster's degree:is_first_childyes               -1.484 0.138693    
## parent_educsome college:is_first_childyes                   2.456 0.014533 *  
## parent_educsome high school:is_first_childyes               2.026 0.043506 *  
## parent_educbachelor's degree:transport_meansschool_bus      0.290 0.771982    
## parent_educhigh school:transport_meansschool_bus            0.678 0.497920    
## parent_educmaster's degree:transport_meansschool_bus        0.362 0.717468    
## parent_educsome college:transport_meansschool_bus          -0.721 0.471520    
## parent_educsome high school:transport_meansschool_bus       1.441 0.150635    
## parent_educbachelor's degree:wkly_study_hours> 10          -0.074 0.941138    
## parent_educhigh school:wkly_study_hours> 10                -0.160 0.872940    
## parent_educmaster's degree:wkly_study_hours> 10            -0.622 0.534578    
## parent_educsome college:wkly_study_hours> 10               -1.338 0.181799    
## parent_educsome high school:wkly_study_hours> 10           -0.780 0.435922    
## parent_educbachelor's degree:wkly_study_hours10-May        -0.511 0.609403    
## parent_educhigh school:wkly_study_hours10-May              -0.785 0.433272    
## parent_educmaster's degree:wkly_study_hours10-May          -1.044 0.297081    
## parent_educsome college:wkly_study_hours10-May             -1.920 0.055680 .  
## parent_educsome high school:wkly_study_hours10-May         -0.322 0.747860    
## parent_educbachelor's degree:math_score                    -1.802 0.072457 .  
## parent_educhigh school:math_score                          -0.874 0.382598    
## parent_educmaster's degree:math_score                       0.442 0.658912    
## parent_educsome college:math_score                          0.058 0.953783    
## parent_educsome high school:math_score                     -0.382 0.702748    
## parent_educbachelor's degree:reading_score                  1.648 0.100376    
## parent_educhigh school:reading_score                        0.432 0.665928    
## parent_educmaster's degree:reading_score                   -0.440 0.659957    
## parent_educsome college:reading_score                       0.240 0.810322    
## parent_educsome high school:reading_score                   0.432 0.666207    
## lunch_typestandard:test_prepnone                            0.247 0.804865    
## lunch_typestandard:parent_marital_statusmarried            -0.324 0.746205    
## lunch_typestandard:parent_marital_statussingle             -1.224 0.221656    
## lunch_typestandard:parent_marital_statuswidowed             0.082 0.934829    
## lunch_typestandard:practice_sportregularly                  0.440 0.660361    
## lunch_typestandard:practice_sportsometimes                  1.160 0.246956    
## lunch_typestandard:is_first_childyes                       -1.064 0.288093    
## lunch_typestandard:transport_meansschool_bus               -0.221 0.824926    
## lunch_typestandard:wkly_study_hours> 10                    -0.284 0.776475    
## lunch_typestandard:wkly_study_hours10-May                   0.350 0.726219    
## lunch_typestandard:math_score                               0.587 0.557320    
## lunch_typestandard:reading_score                           -0.075 0.940565    
## test_prepnone:parent_marital_statusmarried                 -2.633 0.008849 ** 
## test_prepnone:parent_marital_statussingle                  -2.183 0.029715 *  
## test_prepnone:parent_marital_statuswidowed                 -0.711 0.477729    
## test_prepnone:practice_sportregularly                       0.208 0.835044    
## test_prepnone:practice_sportsometimes                       1.284 0.199991    
## test_prepnone:is_first_childyes                            -1.165 0.244915    
## test_prepnone:transport_meansschool_bus                     1.903 0.057941 .  
## test_prepnone:wkly_study_hours> 10                          0.085 0.932085    
## test_prepnone:wkly_study_hours10-May                        0.524 0.600519    
## test_prepnone:math_score                                   -0.144 0.885844    
## test_prepnone:reading_score                                 0.347 0.728664    
## parent_marital_statusmarried:practice_sportregularly       -0.641 0.522028    
## parent_marital_statussingle:practice_sportregularly        -1.254 0.210869    
## parent_marital_statuswidowed:practice_sportregularly       -0.268 0.788808    
## parent_marital_statusmarried:practice_sportsometimes       -0.223 0.823464    
## parent_marital_statussingle:practice_sportsometimes        -1.168 0.243438    
## parent_marital_statuswidowed:practice_sportsometimes           NA       NA    
## parent_marital_statusmarried:is_first_childyes             -0.326 0.744549    
## parent_marital_statussingle:is_first_childyes              -0.319 0.750281    
## parent_marital_statuswidowed:is_first_childyes              0.782 0.434517    
## parent_marital_statusmarried:transport_meansschool_bus     -0.384 0.701456    
## parent_marital_statussingle:transport_meansschool_bus       0.748 0.455143    
## parent_marital_statuswidowed:transport_meansschool_bus     -0.413 0.679890    
## parent_marital_statusmarried:wkly_study_hours> 10           0.063 0.950174    
## parent_marital_statussingle:wkly_study_hours> 10            0.552 0.581417    
## parent_marital_statuswidowed:wkly_study_hours> 10              NA       NA    
## parent_marital_statusmarried:wkly_study_hours10-May         2.287 0.022780 *  
## parent_marital_statussingle:wkly_study_hours10-May          2.941 0.003499 ** 
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## parent_marital_statusmarried:math_score                     0.270 0.787397    
## parent_marital_statussingle:math_score                     -0.715 0.475217    
## parent_marital_statuswidowed:math_score                        NA       NA    
## parent_marital_statusmarried:reading_score                 -0.635 0.525774    
## parent_marital_statussingle:reading_score                   0.354 0.723458    
## parent_marital_statuswidowed:reading_score                     NA       NA    
## practice_sportregularly:is_first_childyes                  -1.428 0.154105    
## practice_sportsometimes:is_first_childyes                  -0.770 0.441802    
## practice_sportregularly:transport_meansschool_bus           0.744 0.457620    
## practice_sportsometimes:transport_meansschool_bus           0.591 0.554975    
## practice_sportregularly:wkly_study_hours> 10                0.959 0.338040    
## practice_sportsometimes:wkly_study_hours> 10                0.209 0.834632    
## practice_sportregularly:wkly_study_hours10-May             -0.028 0.977863    
## practice_sportsometimes:wkly_study_hours10-May             -0.580 0.561972    
## practice_sportregularly:math_score                          0.351 0.726157    
## practice_sportsometimes:math_score                          0.054 0.956995    
## practice_sportregularly:reading_score                       0.165 0.868917    
## practice_sportsometimes:reading_score                       0.521 0.602453    
## is_first_childyes:transport_meansschool_bus                -0.590 0.555756    
## is_first_childyes:wkly_study_hours> 10                      1.131 0.258956    
## is_first_childyes:wkly_study_hours10-May                    1.593 0.111981    
## is_first_childyes:math_score                               -0.982 0.326904    
## is_first_childyes:reading_score                             0.674 0.500566    
## transport_meansschool_bus:wkly_study_hours> 10             -0.066 0.947202    
## transport_meansschool_bus:wkly_study_hours10-May           -0.997 0.319290    
## transport_meansschool_bus:math_score                        0.645 0.519614    
## transport_meansschool_bus:reading_score                     0.707 0.480179    
## wkly_study_hours> 10:math_score                             1.127 0.260666    
## wkly_study_hours10-May:math_score                          -0.029 0.977206    
## wkly_study_hours> 10:reading_score                         -1.507 0.132714    
## wkly_study_hours10-May:reading_score                       -0.209 0.834897    
## math_score:reading_score                                   -2.024 0.043746 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.297 on 340 degrees of freedom
## Multiple R-squared:  0.974,  Adjusted R-squared:  0.9549 
## F-statistic: 51.12 on 249 and 340 DF,  p-value: < 2.2e-16
stepwise_model_write2 <- step(full_fit_write2, direction = "both", trace = 1)
## Start:  AIC=1582.41
## writing_score ~ (gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score)^2
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_educ:wkly_study_hours           10    62.949 3757.9 1572.4
## - gender:parent_educ                      5    22.786 3717.7 1576.0
## - ethnic_group:test_prep                  4    19.882 3714.8 1577.6
## - parent_educ:reading_score               5    34.925 3729.8 1578.0
## - practice_sport:wkly_study_hours         4    25.790 3720.7 1578.5
## - ethnic_group:reading_score              4    25.971 3720.9 1578.5
## - gender:practice_sport                   2     0.852 3695.8 1578.5
## - parent_marital_status:is_first_child    2     1.250 3696.2 1578.6
## - parent_marital_status:practice_sport    4    26.525 3721.4 1578.6
## - test_prep:wkly_study_hours              2     3.799 3698.7 1579.0
## - lunch_type:wkly_study_hours             2     4.745 3699.7 1579.2
## - practice_sport:math_score               2     4.955 3699.9 1579.2
## - practice_sport:transport_means          2     6.023 3700.9 1579.4
## - practice_sport:reading_score            2     7.373 3702.3 1579.6
## - parent_educ:math_score                  5    49.405 3744.3 1580.2
## - lunch_type:reading_score                1     0.061 3695.0 1580.4
## - gender:lunch_type                       1     0.099 3695.0 1580.4
## - test_prep:math_score                    1     0.224 3695.1 1580.4
## - lunch_type:transport_means              1     0.533 3695.5 1580.5
## - transport_means:wkly_study_hours        2    13.188 3708.1 1580.5
## - lunch_type:test_prep                    1     0.664 3695.6 1580.5
## - gender:test_prep                        1     1.015 3695.9 1580.6
## - parent_educ:lunch_type                  5    51.531 3746.5 1580.6
## - test_prep:reading_score                 1     1.310 3696.2 1580.6
## - gender:transport_means                  1     1.619 3696.5 1580.7
## - gender:wkly_study_hours                 2    15.457 3710.4 1580.9
## - parent_educ:transport_means             5    53.997 3748.9 1581.0
## - lunch_type:math_score                   1     3.750 3698.7 1581.0
## - is_first_child:transport_means          1     3.780 3698.7 1581.0
## - ethnic_group:transport_means            4    41.700 3736.6 1581.0
## - transport_means:math_score              1     4.516 3699.4 1581.1
## - is_first_child:reading_score            1     4.941 3699.9 1581.2
## - transport_means:reading_score           1     5.429 3700.3 1581.3
## - wkly_study_hours:math_score             2    18.912 3713.8 1581.4
## - gender:math_score                       1     7.562 3702.5 1581.6
## - lunch_type:practice_sport               2    21.534 3716.5 1581.8
## - parent_marital_status:math_score        2    22.471 3717.4 1582.0
## - parent_marital_status:reading_score     2    22.811 3717.7 1582.0
## - lunch_type:parent_marital_status        2    22.922 3717.8 1582.1
## - is_first_child:math_score               1    10.475 3705.4 1582.1
## - parent_marital_status:transport_means   2    23.343 3718.3 1582.1
## - gender:parent_marital_status            2    23.417 3718.3 1582.1
## - gender:is_first_child                   1    10.965 3705.9 1582.2
## - lunch_type:is_first_child               1    12.302 3707.2 1582.4
## <none>                                                3694.9 1582.4
## - parent_educ:test_prep                   5    63.715 3758.6 1582.5
## - gender:ethnic_group                     4    51.066 3746.0 1582.5
## - test_prep:is_first_child                1    14.745 3709.7 1582.8
## - wkly_study_hours:reading_score          2    27.420 3722.3 1582.8
## - ethnic_group:is_first_child             4    53.175 3748.1 1582.8
## - is_first_child:wkly_study_hours         2    28.963 3723.9 1583.0
## - ethnic_group:math_score                 4    55.062 3750.0 1583.1
## - parent_educ:parent_marital_status      11   145.213 3840.1 1583.2
## - ethnic_group:practice_sport             8   108.662 3803.6 1583.5
## - practice_sport:is_first_child           2    32.316 3727.2 1583.5
## - gender:reading_score                    1    22.667 3717.6 1584.0
## - test_prep:practice_sport                2    46.200 3741.1 1585.7
## - ethnic_group:parent_marital_status      8   125.322 3820.2 1586.1
## - test_prep:transport_means               1    39.338 3734.3 1586.7
## - math_score:reading_score                1    44.522 3739.4 1587.5
## - ethnic_group:parent_educ               20   302.255 3997.2 1588.8
## - test_prep:parent_marital_status         2    76.280 3771.2 1590.5
## - parent_educ:practice_sport             10   187.276 3882.2 1591.6
## - parent_marital_status:wkly_study_hours  4   111.531 3806.5 1592.0
## - ethnic_group:wkly_study_hours           8   176.795 3871.7 1594.0
## - ethnic_group:lunch_type                 4   125.572 3820.5 1594.1
## - parent_educ:is_first_child              5   151.702 3846.6 1596.2
## 
## Step:  AIC=1572.38
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:parent_educ + gender:lunch_type + 
##     gender:test_prep + gender:parent_marital_status + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:math_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + ethnic_group:reading_score + parent_educ:lunch_type + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:math_score + 
##     parent_marital_status:reading_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:parent_educ                      5    27.583 3785.5 1566.7
## - parent_educ:reading_score               5    31.853 3789.7 1567.4
## - ethnic_group:reading_score              4    22.722 3780.6 1567.9
## - practice_sport:wkly_study_hours         4    23.202 3781.1 1568.0
## - parent_marital_status:practice_sport    4    23.527 3781.4 1568.1
## - gender:practice_sport                   2     0.743 3758.6 1568.5
## - parent_marital_status:is_first_child    2     1.305 3759.2 1568.6
## - test_prep:wkly_study_hours              2     1.619 3759.5 1568.6
## - ethnic_group:test_prep                  4    28.611 3786.5 1568.8
## - practice_sport:transport_means          2     4.866 3762.7 1569.1
## - parent_educ:math_score                  5    44.454 3802.3 1569.3
## - practice_sport:reading_score            2     6.715 3764.6 1569.4
## - lunch_type:wkly_study_hours             2     7.121 3765.0 1569.5
## - practice_sport:math_score               2     7.826 3765.7 1569.6
## - gender:wkly_study_hours                 2     9.696 3767.6 1569.9
## - lunch_type:transport_means              1     0.019 3757.9 1570.4
## - test_prep:math_score                    1     0.028 3757.9 1570.4
## - lunch_type:test_prep                    1     0.093 3758.0 1570.4
## - lunch_type:reading_score                1     0.123 3758.0 1570.4
## - gender:lunch_type                       1     0.239 3758.1 1570.4
## - gender:test_prep                        1     0.286 3758.2 1570.4
## - test_prep:reading_score                 1     0.641 3758.5 1570.5
## - ethnic_group:transport_means            4    39.439 3797.3 1570.5
## - gender:transport_means                  1     2.277 3760.1 1570.7
## - transport_means:math_score              1     3.428 3761.3 1570.9
## - is_first_child:transport_means          1     3.540 3761.4 1570.9
## - parent_educ:transport_means             5    54.937 3812.8 1570.9
## - lunch_type:math_score                   1     3.629 3761.5 1571.0
## - transport_means:wkly_study_hours        2    16.562 3774.4 1571.0
## - is_first_child:reading_score            1     5.275 3763.1 1571.2
## - wkly_study_hours:math_score             2    18.457 3776.3 1571.3
## - parent_marital_status:transport_means   2    19.317 3777.2 1571.4
## - transport_means:reading_score           1     6.841 3764.7 1571.5
## - lunch_type:practice_sport               2    19.837 3777.7 1571.5
## - gender:ethnic_group                     4    46.794 3804.7 1571.7
## - parent_marital_status:math_score        2    21.227 3779.1 1571.7
## - is_first_child:wkly_study_hours         2    21.681 3779.6 1571.8
## - gender:math_score                       1     9.244 3767.1 1571.8
## - gender:is_first_child                   1     9.510 3767.4 1571.9
## - parent_marital_status:reading_score     2    22.326 3780.2 1571.9
## - lunch_type:parent_marital_status        2    22.805 3780.7 1572.0
## - ethnic_group:is_first_child             4    48.874 3806.7 1572.0
## - is_first_child:math_score               1    11.075 3768.9 1572.1
## - test_prep:is_first_child                1    11.352 3769.2 1572.2
## <none>                                                3757.9 1572.4
## - ethnic_group:math_score                 4    51.893 3809.8 1572.5
## - wkly_study_hours:reading_score          2    26.204 3784.1 1572.5
## - gender:parent_marital_status            2    26.468 3784.3 1572.5
## - parent_educ:test_prep                   5    65.923 3823.8 1572.6
## - parent_educ:lunch_type                  5    69.778 3827.6 1573.2
## - practice_sport:is_first_child           2    31.312 3789.2 1573.3
## - ethnic_group:practice_sport             8   110.773 3868.6 1573.5
## - lunch_type:is_first_child               1    20.594 3778.5 1573.6
## - parent_educ:parent_marital_status      11   154.814 3912.7 1574.2
## - gender:reading_score                    1    24.469 3782.3 1574.2
## - test_prep:practice_sport                2    47.385 3805.3 1575.8
## - ethnic_group:parent_marital_status      8   128.301 3886.2 1576.2
## - test_prep:transport_means               1    37.677 3795.5 1576.3
## - ethnic_group:parent_educ               20   295.100 4053.0 1577.0
## - math_score:reading_score                1    51.162 3809.0 1578.3
## - parent_marital_status:wkly_study_hours  4   106.504 3864.4 1580.9
## - ethnic_group:wkly_study_hours           8   162.721 3920.6 1581.4
## - parent_educ:practice_sport             10   189.415 3947.3 1581.4
## - test_prep:parent_marital_status         2    84.198 3842.1 1581.5
## + parent_educ:wkly_study_hours           10    62.949 3694.9 1582.4
## - ethnic_group:lunch_type                 4   126.428 3884.3 1583.9
## - parent_educ:is_first_child              5   144.454 3902.3 1584.6
## 
## Step:  AIC=1566.69
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:math_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + ethnic_group:reading_score + parent_educ:lunch_type + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:math_score + 
##     parent_marital_status:reading_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:reading_score              4    21.848 3807.3 1562.1
## - parent_educ:reading_score               5    35.036 3820.5 1562.1
## - parent_marital_status:practice_sport    4    22.902 3808.4 1562.2
## - practice_sport:wkly_study_hours         4    24.329 3809.8 1562.5
## - gender:practice_sport                   2     0.752 3786.2 1562.8
## - parent_marital_status:is_first_child    2     1.148 3786.6 1562.9
## - test_prep:wkly_study_hours              2     2.059 3787.5 1563.0
## - ethnic_group:test_prep                  4    27.986 3813.4 1563.0
## - parent_educ:math_score                  5    42.626 3828.1 1563.3
## - practice_sport:transport_means          2     4.323 3789.8 1563.4
## - lunch_type:wkly_study_hours             2     7.364 3792.8 1563.8
## - practice_sport:reading_score            2     7.840 3793.3 1563.9
## - practice_sport:math_score               2     7.855 3793.3 1563.9
## - gender:wkly_study_hours                 2    10.753 3796.2 1564.4
## - ethnic_group:transport_means            4    37.803 3823.3 1564.5
## - lunch_type:test_prep                    1     0.035 3785.5 1564.7
## - lunch_type:transport_means              1     0.119 3785.6 1564.7
## - test_prep:math_score                    1     0.127 3785.6 1564.7
## - lunch_type:reading_score                1     0.344 3785.8 1564.7
## - gender:test_prep                        1     0.611 3786.1 1564.8
## - gender:lunch_type                       1     0.838 3786.3 1564.8
## - test_prep:reading_score                 1     0.959 3786.4 1564.8
## - transport_means:math_score              1     1.827 3787.3 1565.0
## - is_first_child:transport_means          1     2.402 3787.9 1565.1
## - transport_means:wkly_study_hours        2    15.509 3801.0 1565.1
## - parent_educ:transport_means             5    54.410 3839.9 1565.1
## - wkly_study_hours:math_score             2    15.608 3801.1 1565.1
## - parent_marital_status:transport_means   2    15.888 3801.3 1565.2
## - gender:transport_means                  1     3.189 3788.6 1565.2
## - lunch_type:math_score                   1     5.456 3790.9 1565.5
## - is_first_child:reading_score            1     6.047 3791.5 1565.6
## - lunch_type:practice_sport               2    19.737 3805.2 1565.8
## - is_first_child:wkly_study_hours         2    19.752 3805.2 1565.8
## - parent_educ:test_prep                   5    58.890 3844.3 1565.8
## - gender:ethnic_group                     4    46.932 3832.4 1566.0
## - lunch_type:parent_marital_status        2    21.839 3807.3 1566.1
## - gender:is_first_child                   1     9.186 3794.6 1566.1
## - parent_marital_status:math_score        2    22.363 3807.8 1566.2
## - transport_means:reading_score           1     9.527 3795.0 1566.2
## - wkly_study_hours:reading_score          2    23.884 3809.3 1566.4
## - ethnic_group:is_first_child             4    50.203 3835.7 1566.5
## - ethnic_group:math_score                 4    50.587 3836.0 1566.5
## - parent_marital_status:reading_score     2    24.912 3810.4 1566.6
## - gender:math_score                       1    12.668 3798.1 1566.7
## - is_first_child:math_score               1    12.848 3798.3 1566.7
## <none>                                                3785.5 1566.7
## - test_prep:is_first_child                1    14.905 3800.4 1567.0
## - gender:parent_marital_status            2    30.128 3815.6 1567.4
## - practice_sport:is_first_child           2    31.109 3816.6 1567.5
## - parent_educ:lunch_type                  5    70.249 3855.7 1567.5
## - lunch_type:is_first_child               1    20.847 3806.3 1567.9
## - parent_educ:parent_marital_status      11   153.429 3938.9 1568.1
## - ethnic_group:practice_sport             8   118.110 3903.6 1568.8
## - gender:reading_score                    1    32.500 3818.0 1569.7
## - test_prep:practice_sport                2    45.736 3831.2 1569.8
## - test_prep:transport_means               1    41.797 3827.2 1571.2
## - ethnic_group:parent_educ               20   297.789 4083.2 1571.4
## - ethnic_group:parent_marital_status      8   137.109 3922.6 1571.7
## + gender:parent_educ                      5    27.583 3757.9 1572.4
## - math_score:reading_score                1    60.046 3845.5 1574.0
## - parent_marital_status:wkly_study_hours  4   105.657 3891.1 1574.9
## - parent_educ:practice_sport             10   188.025 3973.5 1575.3
## + parent_educ:wkly_study_hours           10    67.747 3717.7 1576.0
## - test_prep:parent_marital_status         2    86.704 3872.2 1576.0
## - ethnic_group:wkly_study_hours           8   167.590 3953.0 1576.2
## - ethnic_group:lunch_type                 4   126.481 3911.9 1578.1
## - parent_educ:is_first_child              5   161.474 3946.9 1581.3
## 
## Step:  AIC=1562.09
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:math_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:math_score + 
##     parent_marital_status:reading_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_marital_status:practice_sport    4    19.517 3826.8 1557.1
## - practice_sport:wkly_study_hours         4    22.287 3829.6 1557.5
## - gender:practice_sport                   2     0.727 3808.0 1558.2
## - parent_marital_status:is_first_child    2     0.835 3808.1 1558.2
## - test_prep:wkly_study_hours              2     3.358 3810.7 1558.6
## - parent_educ:reading_score               5    42.868 3850.2 1558.7
## - lunch_type:wkly_study_hours             2     5.668 3813.0 1559.0
## - ethnic_group:test_prep                  4    31.714 3839.0 1559.0
## - practice_sport:transport_means          2     5.795 3813.1 1559.0
## - parent_educ:math_score                  5    46.199 3853.5 1559.2
## - gender:wkly_study_hours                 2     7.331 3814.6 1559.2
## - practice_sport:math_score               2     7.774 3815.1 1559.3
## - practice_sport:reading_score            2     8.155 3815.5 1559.3
## - lunch_type:test_prep                    1     0.000 3807.3 1560.1
## - test_prep:math_score                    1     0.104 3807.4 1560.1
## - lunch_type:transport_means              1     0.201 3807.5 1560.1
## - lunch_type:reading_score                1     0.228 3807.5 1560.1
## - gender:test_prep                        1     0.575 3807.9 1560.2
## - wkly_study_hours:math_score             2    13.544 3820.8 1560.2
## - gender:lunch_type                       1     0.681 3808.0 1560.2
## - test_prep:reading_score                 1     0.966 3808.3 1560.2
## - parent_marital_status:transport_means   2    14.336 3821.6 1560.3
## - transport_means:wkly_study_hours        2    14.614 3821.9 1560.3
## - is_first_child:transport_means          1     2.089 3809.4 1560.4
## - gender:transport_means                  1     2.433 3809.7 1560.5
## - transport_means:math_score              1     2.986 3810.3 1560.5
## - lunch_type:practice_sport               2    16.302 3823.6 1560.6
## - is_first_child:reading_score            1     4.542 3811.8 1560.8
## - gender:ethnic_group                     4    43.711 3851.0 1560.8
## - ethnic_group:transport_means            4    44.106 3851.4 1560.9
## - parent_educ:test_prep                   5    57.889 3865.2 1561.0
## - parent_educ:transport_means             5    57.975 3865.3 1561.0
## - is_first_child:wkly_study_hours         2    19.406 3826.7 1561.1
## - transport_means:reading_score           1     6.499 3813.8 1561.1
## - lunch_type:math_score                   1     6.660 3814.0 1561.1
## - lunch_type:parent_marital_status        2    20.900 3828.2 1561.3
## - wkly_study_hours:reading_score          2    21.824 3829.1 1561.5
## - gender:is_first_child                   1     9.344 3816.6 1561.5
## - ethnic_group:is_first_child             4    48.365 3855.7 1561.5
## - parent_educ:parent_marital_status      11   142.875 3950.2 1561.8
## - parent_marital_status:math_score        2    25.313 3832.6 1562.0
## - is_first_child:math_score               1    12.668 3820.0 1562.0
## <none>                                                3807.3 1562.1
## - parent_marital_status:reading_score     2    27.775 3835.1 1562.4
## - test_prep:is_first_child                1    15.013 3822.3 1562.4
## - gender:math_score                       1    15.416 3822.7 1562.5
## - parent_educ:lunch_type                  5    69.639 3876.9 1562.8
## - lunch_type:is_first_child               1    18.473 3825.8 1562.9
## - gender:parent_marital_status            2    33.282 3840.6 1563.2
## - ethnic_group:practice_sport             8   114.716 3922.0 1563.6
## - practice_sport:is_first_child           2    36.899 3844.2 1563.8
## - ethnic_group:math_score                 4    63.747 3871.0 1563.9
## - test_prep:practice_sport                2    41.275 3848.6 1564.5
## - ethnic_group:parent_marital_status      8   130.914 3938.2 1566.0
## - gender:reading_score                    1    38.958 3846.3 1566.1
## + ethnic_group:reading_score              4    21.848 3785.5 1566.7
## - test_prep:transport_means               1    44.252 3851.6 1566.9
## + gender:parent_educ                      5    26.709 3780.6 1567.9
## - ethnic_group:parent_educ               20   312.387 4119.7 1568.6
## - parent_educ:practice_sport             10   183.206 3990.5 1569.8
## - parent_marital_status:wkly_study_hours  4   107.527 3914.8 1570.5
## - test_prep:parent_marital_status         2    81.137 3888.4 1570.5
## - math_score:reading_score                1    69.969 3877.3 1570.8
## - ethnic_group:lunch_type                 4   113.388 3920.7 1571.4
## + parent_educ:wkly_study_hours           10    63.592 3743.7 1572.2
## - ethnic_group:wkly_study_hours           8   178.272 3985.6 1573.1
## - parent_educ:is_first_child              5   156.726 3964.0 1575.9
## 
## Step:  AIC=1557.1
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:math_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:math_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - practice_sport:wkly_study_hours         4    18.025 3844.8 1551.9
## - gender:practice_sport                   2     1.095 3827.9 1553.3
## - parent_marital_status:is_first_child    2     1.795 3828.6 1553.4
## - ethnic_group:test_prep                  4    30.097 3856.9 1553.7
## - lunch_type:wkly_study_hours             2     4.814 3831.6 1553.8
## - test_prep:wkly_study_hours              2     4.999 3831.8 1553.9
## - practice_sport:transport_means          2     5.016 3831.8 1553.9
## - parent_educ:math_score                  5    46.122 3872.9 1554.2
## - parent_educ:reading_score               5    46.464 3873.3 1554.2
## - gender:wkly_study_hours                 2     7.345 3834.2 1554.2
## - practice_sport:reading_score            2     8.089 3834.9 1554.3
## - practice_sport:math_score               2     8.347 3835.2 1554.4
## - wkly_study_hours:math_score             2    11.873 3838.7 1554.9
## - lunch_type:test_prep                    1     0.018 3826.8 1555.1
## - test_prep:math_score                    1     0.094 3826.9 1555.1
## - lunch_type:transport_means              1     0.172 3827.0 1555.1
## - lunch_type:reading_score                1     0.229 3827.0 1555.1
## - gender:lunch_type                       1     0.259 3827.1 1555.1
## - parent_marital_status:transport_means   2    13.526 3840.3 1555.2
## - gender:test_prep                        1     0.626 3827.4 1555.2
## - test_prep:reading_score                 1     0.754 3827.6 1555.2
## - lunch_type:practice_sport               2    14.226 3841.0 1555.3
## - gender:transport_means                  1     1.664 3828.5 1555.4
## - parent_educ:test_prep                   5    54.465 3881.3 1555.4
## - is_first_child:transport_means          1     2.833 3829.7 1555.5
## - transport_means:wkly_study_hours        2    15.923 3842.7 1555.5
## - is_first_child:reading_score            1     3.373 3830.2 1555.6
## - transport_means:math_score              1     3.975 3830.8 1555.7
## - parent_educ:parent_marital_status      12   150.213 3977.0 1555.8
## - is_first_child:wkly_study_hours         2    17.974 3844.8 1555.9
## - parent_educ:transport_means             5    57.327 3884.1 1555.9
## - transport_means:reading_score           1     5.640 3832.5 1556.0
## - gender:ethnic_group                     4    45.354 3872.2 1556.0
## - ethnic_group:is_first_child             4    45.507 3872.3 1556.1
## - lunch_type:math_score                   1     6.782 3833.6 1556.2
## - wkly_study_hours:reading_score          2    19.985 3846.8 1556.2
## - gender:is_first_child                   1     8.811 3835.6 1556.5
## - lunch_type:parent_marital_status        2    22.113 3848.9 1556.5
## - ethnic_group:transport_means            4    48.311 3875.1 1556.5
## - ethnic_group:practice_sport             8   103.054 3929.9 1556.8
## - is_first_child:math_score               1    12.164 3839.0 1557.0
## <none>                                                3826.8 1557.1
## - parent_marital_status:math_score        2    26.649 3853.5 1557.2
## - test_prep:is_first_child                1    15.821 3842.6 1557.5
## - gender:math_score                       1    16.268 3843.1 1557.6
## - practice_sport:is_first_child           2    29.609 3856.4 1557.7
## - lunch_type:is_first_child               1    17.216 3844.0 1557.8
## - parent_marital_status:reading_score     2    30.657 3857.5 1557.8
## - parent_educ:lunch_type                  5    73.755 3900.6 1558.4
## - gender:parent_marital_status            2    36.006 3862.8 1558.6
## - ethnic_group:math_score                 4    62.740 3889.6 1558.7
## - test_prep:practice_sport                2    38.231 3865.0 1559.0
## - ethnic_group:parent_marital_status      8   131.658 3958.5 1561.1
## - gender:reading_score                    1    39.188 3866.0 1561.1
## - test_prep:transport_means               1    42.256 3869.1 1561.6
## + parent_marital_status:practice_sport    4    19.517 3807.3 1562.1
## + ethnic_group:reading_score              4    18.462 3808.4 1562.2
## + gender:parent_educ                      5    26.276 3800.5 1563.0
## - ethnic_group:parent_educ               20   311.069 4137.9 1563.2
## - test_prep:parent_marital_status         2    74.843 3901.7 1564.5
## - parent_educ:practice_sport             10   186.449 4013.3 1565.2
## - ethnic_group:lunch_type                 4   112.206 3939.0 1566.2
## - parent_marital_status:wkly_study_hours  4   112.796 3939.6 1566.2
## - math_score:reading_score                1    73.484 3900.3 1566.3
## - ethnic_group:wkly_study_hours           8   172.145 3999.0 1567.1
## + parent_educ:wkly_study_hours           10    61.882 3764.9 1567.5
## - parent_educ:is_first_child              5   153.512 3980.3 1570.3
## 
## Step:  AIC=1551.88
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:math_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:math_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:practice_sport                   2     1.082 3845.9 1548.0
## - parent_marital_status:is_first_child    2     1.118 3846.0 1548.0
## - ethnic_group:test_prep                  4    30.233 3875.1 1548.5
## - practice_sport:transport_means          2     4.509 3849.4 1548.6
## - lunch_type:wkly_study_hours             2     4.510 3849.4 1548.6
## - test_prep:wkly_study_hours              2     5.395 3850.2 1548.7
## - gender:wkly_study_hours                 2     9.380 3854.2 1549.3
## - practice_sport:reading_score            2    10.580 3855.4 1549.5
## - parent_educ:parent_marital_status      12   144.908 3989.7 1549.7
## - parent_marital_status:transport_means   2    12.048 3856.9 1549.7
## - practice_sport:math_score               2    12.381 3857.2 1549.8
## - test_prep:math_score                    1     0.052 3844.9 1549.9
## - lunch_type:test_prep                    1     0.069 3844.9 1549.9
## - parent_educ:math_score                  5    52.567 3897.4 1549.9
## - lunch_type:transport_means              1     0.174 3845.0 1549.9
## - gender:test_prep                        1     0.285 3845.1 1549.9
## - lunch_type:practice_sport               2    13.378 3858.2 1549.9
## - test_prep:reading_score                 1     0.407 3845.2 1549.9
## - gender:lunch_type                       1     0.441 3845.3 1549.9
## - lunch_type:reading_score                1     0.800 3845.6 1550.0
## - parent_educ:reading_score               5    53.793 3898.6 1550.1
## - gender:transport_means                  1     1.347 3846.2 1550.1
## - wkly_study_hours:math_score             2    15.152 3860.0 1550.2
## - is_first_child:reading_score            1     2.575 3847.4 1550.3
## - is_first_child:transport_means          1     2.647 3847.5 1550.3
## - transport_means:wkly_study_hours        2    15.729 3860.6 1550.3
## - parent_educ:transport_means             5    55.877 3900.7 1550.4
## - parent_educ:test_prep                   5    55.907 3900.7 1550.4
## - is_first_child:wkly_study_hours         2    16.988 3861.8 1550.5
## - gender:ethnic_group                     4    43.367 3888.2 1550.5
## - transport_means:reading_score           1     4.536 3849.4 1550.6
## - transport_means:math_score              1     5.108 3850.0 1550.7
## - lunch_type:parent_marital_status        2    19.810 3864.7 1550.9
## - ethnic_group:transport_means            4    48.326 3893.2 1551.2
## - lunch_type:math_score                   1     9.185 3854.0 1551.3
## - gender:is_first_child                   1     9.191 3854.0 1551.3
## - ethnic_group:is_first_child             4    50.004 3894.8 1551.5
## - is_first_child:math_score               1    11.686 3856.5 1551.7
## - wkly_study_hours:reading_score          2    25.142 3870.0 1551.7
## - parent_marital_status:math_score        2    25.758 3870.6 1551.8
## - ethnic_group:practice_sport             8   105.352 3950.2 1551.8
## <none>                                                3844.8 1551.9
## - lunch_type:is_first_child               1    13.769 3858.6 1552.0
## - parent_marital_status:reading_score     2    28.803 3873.6 1552.3
## - practice_sport:is_first_child           2    29.437 3874.3 1552.4
## - test_prep:is_first_child                1    18.211 3863.1 1552.7
## - gender:math_score                       1    18.609 3863.5 1552.7
## - parent_educ:lunch_type                  5    73.363 3918.2 1553.0
## - gender:parent_marital_status            2    34.522 3879.4 1553.2
## - ethnic_group:math_score                 4    64.766 3909.6 1553.7
## - test_prep:practice_sport                2    41.300 3886.1 1554.2
## - test_prep:transport_means               1    35.867 3880.7 1555.3
## - ethnic_group:parent_marital_status      8   134.014 3978.9 1556.1
## - gender:reading_score                    1    40.787 3885.6 1556.1
## - ethnic_group:parent_educ               20   301.369 4146.2 1556.4
## + practice_sport:wkly_study_hours         4    18.025 3826.8 1557.1
## + ethnic_group:reading_score              4    16.858 3828.0 1557.3
## + parent_marital_status:practice_sport    4    15.254 3829.6 1557.5
## + gender:parent_educ                      5    27.218 3817.6 1557.7
## - parent_educ:practice_sport             10   176.617 4021.5 1558.4
## - test_prep:parent_marital_status         2    76.631 3921.5 1559.5
## - parent_marital_status:wkly_study_hours  4   112.107 3956.9 1560.8
## - ethnic_group:lunch_type                 4   113.404 3958.2 1561.0
## - math_score:reading_score                1    74.418 3919.3 1561.2
## - ethnic_group:wkly_study_hours           8   169.579 4014.4 1561.3
## + parent_educ:wkly_study_hours           10    61.641 3783.2 1562.3
## - parent_educ:is_first_child              5   158.255 4003.1 1565.7
## 
## Step:  AIC=1548.04
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + gender:math_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:math_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_marital_status:is_first_child    2     1.019 3846.9 1544.2
## - ethnic_group:test_prep                  4    29.517 3875.4 1544.5
## - practice_sport:transport_means          2     4.532 3850.5 1544.7
## - lunch_type:wkly_study_hours             2     4.774 3850.7 1544.8
## - test_prep:wkly_study_hours              2     5.359 3851.3 1544.9
## - gender:wkly_study_hours                 2     9.739 3855.7 1545.5
## - parent_marital_status:transport_means   2    11.254 3857.2 1545.8
## - parent_educ:parent_marital_status      12   144.358 3990.3 1545.8
## - parent_educ:math_score                  5    52.097 3898.0 1546.0
## - lunch_type:test_prep                    1     0.032 3846.0 1546.0
## - test_prep:math_score                    1     0.060 3846.0 1546.0
## - lunch_type:transport_means              1     0.142 3846.1 1546.1
## - gender:test_prep                        1     0.371 3846.3 1546.1
## - test_prep:reading_score                 1     0.419 3846.3 1546.1
## - gender:lunch_type                       1     0.563 3846.5 1546.1
## - parent_educ:reading_score               5    53.293 3899.2 1546.2
## - lunch_type:reading_score                1     0.836 3846.8 1546.2
## - gender:transport_means                  1     1.264 3847.2 1546.2
## - lunch_type:practice_sport               2    15.034 3861.0 1546.3
## - wkly_study_hours:math_score             2    15.410 3861.3 1546.4
## - is_first_child:reading_score            1     2.619 3848.5 1546.4
## - parent_educ:test_prep                   5    55.173 3901.1 1546.5
## - transport_means:wkly_study_hours        2    15.741 3861.7 1546.5
## - is_first_child:transport_means          1     2.749 3848.7 1546.5
## - is_first_child:wkly_study_hours         2    16.690 3862.6 1546.6
## - gender:ethnic_group                     4    43.210 3889.1 1546.6
## - transport_means:reading_score           1     4.401 3850.3 1546.7
## - parent_educ:transport_means             5    57.717 3903.6 1546.8
## - transport_means:math_score              1     5.277 3851.2 1546.8
## - lunch_type:parent_marital_status        2    19.571 3865.5 1547.0
## - ethnic_group:transport_means            4    48.401 3894.3 1547.4
## - gender:is_first_child                   1     9.365 3855.3 1547.5
## - lunch_type:math_score                   1     9.667 3855.6 1547.5
## - ethnic_group:is_first_child             4    51.091 3897.0 1547.8
## - is_first_child:math_score               1    11.707 3857.6 1547.8
## - parent_marital_status:math_score        2    25.651 3871.6 1548.0
## - wkly_study_hours:reading_score          2    25.887 3871.8 1548.0
## <none>                                                3845.9 1548.0
## - lunch_type:is_first_child               1    13.737 3859.7 1548.2
## - ethnic_group:practice_sport             8   107.799 3953.7 1548.3
## - practice_sport:is_first_child           2    28.719 3874.6 1548.4
## - parent_marital_status:reading_score     2    28.944 3874.9 1548.5
## - practice_sport:reading_score            2    29.338 3875.3 1548.5
## - practice_sport:math_score               2    30.317 3876.2 1548.7
## - test_prep:is_first_child                1    17.830 3863.8 1548.8
## - gender:math_score                       1    18.573 3864.5 1548.9
## - gender:parent_marital_status            2    35.200 3881.1 1549.4
## - parent_educ:lunch_type                  5    74.905 3920.8 1549.4
## - ethnic_group:math_score                 4    65.143 3911.1 1550.0
## - test_prep:practice_sport                2    42.773 3888.7 1550.6
## - test_prep:transport_means               1    35.208 3881.1 1551.4
## + gender:practice_sport                   2     1.082 3844.8 1551.9
## - gender:reading_score                    1    40.794 3886.7 1552.3
## - ethnic_group:parent_marital_status      8   134.792 3980.7 1552.4
## - ethnic_group:parent_educ               20   304.276 4150.2 1553.0
## + practice_sport:wkly_study_hours         4    18.013 3827.9 1553.3
## + ethnic_group:reading_score              4    17.130 3828.8 1553.4
## + parent_marital_status:practice_sport    4    15.684 3830.2 1553.6
## + gender:parent_educ                      5    26.659 3819.3 1553.9
## - parent_educ:practice_sport             10   181.283 4027.2 1555.2
## - test_prep:parent_marital_status         2    76.039 3922.0 1555.6
## - parent_marital_status:wkly_study_hours  4   111.145 3957.1 1556.8
## - math_score:reading_score                1    75.125 3921.1 1557.5
## - ethnic_group:wkly_study_hours           8   169.288 4015.2 1557.5
## - ethnic_group:lunch_type                 4   118.370 3964.3 1557.9
## + parent_educ:wkly_study_hours           10    62.312 3783.6 1558.4
## - parent_educ:is_first_child              5   158.649 4004.6 1561.9
## 
## Step:  AIC=1544.2
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + gender:math_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:math_score + 
##     parent_marital_status:reading_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_educ:parent_marital_status      13   147.779 3994.7 1540.4
## - practice_sport:transport_means          2     4.396 3851.3 1540.9
## - ethnic_group:test_prep                  4    30.876 3877.8 1540.9
## - lunch_type:wkly_study_hours             2     4.712 3851.7 1540.9
## - test_prep:wkly_study_hours              2     5.156 3852.1 1541.0
## - gender:wkly_study_hours                 2     9.699 3856.6 1541.7
## - parent_marital_status:transport_means   2    10.858 3857.8 1541.9
## - parent_educ:math_score                  5    52.088 3899.0 1542.1
## - lunch_type:test_prep                    1     0.029 3847.0 1542.2
## - test_prep:math_score                    1     0.060 3847.0 1542.2
## - lunch_type:transport_means              1     0.147 3847.1 1542.2
## - gender:test_prep                        1     0.351 3847.3 1542.2
## - test_prep:reading_score                 1     0.404 3847.3 1542.3
## - gender:lunch_type                       1     0.632 3847.6 1542.3
## - lunch_type:reading_score                1     0.905 3847.8 1542.3
## - parent_educ:reading_score               5    53.702 3900.6 1542.4
## - gender:transport_means                  1     1.240 3848.2 1542.4
## - lunch_type:practice_sport               2    14.629 3861.6 1542.4
## - transport_means:wkly_study_hours        2    15.129 3862.1 1542.5
## - parent_educ:test_prep                   5    54.802 3901.7 1542.5
## - wkly_study_hours:math_score             2    15.346 3862.3 1542.5
## - is_first_child:reading_score            1     2.719 3849.7 1542.6
## - is_first_child:transport_means          1     2.791 3849.7 1542.6
## - is_first_child:wkly_study_hours         2    16.533 3863.5 1542.7
## - gender:ethnic_group                     4    43.706 3890.6 1542.9
## - transport_means:reading_score           1     4.481 3851.4 1542.9
## - transport_means:math_score              1     5.187 3852.1 1543.0
## - parent_educ:transport_means             5    58.482 3905.4 1543.1
## - lunch_type:parent_marital_status        2    19.377 3866.3 1543.2
## - ethnic_group:transport_means            4    47.555 3894.5 1543.5
## - gender:is_first_child                   1     9.746 3856.7 1543.7
## - lunch_type:math_score                   1    10.005 3856.9 1543.7
## - is_first_child:math_score               1    11.394 3858.3 1543.9
## - wkly_study_hours:reading_score          2    25.453 3872.4 1544.1
## - parent_marital_status:math_score        2    25.778 3872.7 1544.1
## <none>                                                3846.9 1544.2
## - ethnic_group:is_first_child             4    52.718 3899.7 1544.2
## - lunch_type:is_first_child               1    13.501 3860.4 1544.3
## - ethnic_group:practice_sport             8   106.850 3953.8 1544.4
## - practice_sport:is_first_child           2    28.474 3875.4 1544.5
## - parent_marital_status:reading_score     2    28.823 3875.8 1544.6
## - practice_sport:reading_score            2    29.296 3876.2 1544.7
## - practice_sport:math_score               2    30.332 3877.3 1544.8
## - test_prep:is_first_child                1    17.346 3864.3 1544.8
## - gender:math_score                       1    18.836 3865.8 1545.1
## - gender:parent_marital_status            2    34.722 3881.7 1545.5
## - parent_educ:lunch_type                  5    75.245 3922.2 1545.6
## - ethnic_group:math_score                 4    64.406 3911.3 1546.0
## - ethnic_group:parent_marital_status      9   135.974 3982.9 1546.7
## - test_prep:practice_sport                2    43.546 3890.5 1546.8
## - test_prep:transport_means               1    34.828 3881.8 1547.5
## + parent_marital_status:is_first_child    2     1.019 3845.9 1548.0
## + gender:practice_sport                   2     0.983 3846.0 1548.0
## - gender:reading_score                    1    40.892 3887.8 1548.4
## - ethnic_group:parent_educ               20   305.056 4152.0 1549.2
## + practice_sport:wkly_study_hours         4    17.389 3829.6 1549.5
## + ethnic_group:reading_score              4    16.843 3830.1 1549.6
## + parent_marital_status:practice_sport    4    16.397 3830.5 1549.7
## + gender:parent_educ                      5    26.998 3819.9 1550.0
## - parent_educ:practice_sport             10   181.707 4028.7 1551.4
## - test_prep:parent_marital_status         2    76.167 3923.1 1551.8
## - parent_marital_status:wkly_study_hours  4   111.330 3958.3 1553.0
## - math_score:reading_score                1    75.584 3922.5 1553.7
## - ethnic_group:wkly_study_hours           8   170.355 4017.3 1553.8
## - ethnic_group:lunch_type                 4   119.129 3966.1 1554.2
## + parent_educ:wkly_study_hours           10    62.794 3784.1 1554.5
## - parent_educ:is_first_child              5   161.530 4008.5 1558.5
## 
## Step:  AIC=1540.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + gender:math_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:math_score + 
##     parent_marital_status:reading_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_educ:test_prep                   5    34.478 4029.2 1535.5
## - parent_marital_status:transport_means   3    12.388 4007.1 1536.3
## - gender:wkly_study_hours                 2     6.072 4000.8 1537.3
## - lunch_type:wkly_study_hours             2     6.434 4001.2 1537.4
## - ethnic_group:test_prep                  4    34.744 4029.5 1537.5
## - practice_sport:transport_means          2     8.185 4002.9 1537.7
## - parent_marital_status:math_score        3    22.557 4017.3 1537.8
## - test_prep:wkly_study_hours              2     9.134 4003.9 1537.8
## - wkly_study_hours:math_score             2     9.339 4004.1 1537.8
## - ethnic_group:parent_educ               20   261.812 4256.5 1537.9
## - is_first_child:wkly_study_hours         2    10.744 4005.5 1538.0
## - ethnic_group:practice_sport             8    93.525 4088.2 1538.1
## - parent_marital_status:reading_score     3    25.333 4020.1 1538.2
## - lunch_type:parent_marital_status        3    25.859 4020.6 1538.2
## - lunch_type:practice_sport               2    12.628 4007.3 1538.3
## - gender:test_prep                        1     0.037 3994.8 1538.4
## - test_prep:reading_score                 1     0.118 3994.8 1538.5
## - lunch_type:transport_means              1     0.173 3994.9 1538.5
## - test_prep:math_score                    1     0.194 3994.9 1538.5
## - is_first_child:transport_means          1     0.311 3995.0 1538.5
## - is_first_child:reading_score            1     0.402 3995.1 1538.5
## - lunch_type:test_prep                    1     0.439 3995.2 1538.5
## - gender:lunch_type                       1     0.746 3995.5 1538.5
## - gender:transport_means                  1     0.761 3995.5 1538.5
## - wkly_study_hours:reading_score          2    14.891 4009.6 1538.6
## - transport_means:reading_score           1     3.555 3998.3 1539.0
## - ethnic_group:parent_marital_status     11   141.689 4136.4 1539.0
## - gender:parent_marital_status            3    31.061 4025.8 1539.0
## - lunch_type:reading_score                1     4.323 3999.0 1539.1
## - is_first_child:math_score               1     4.379 3999.1 1539.1
## - gender:is_first_child                   1     4.515 3999.2 1539.1
## - transport_means:math_score              1     5.313 4000.0 1539.2
## - ethnic_group:transport_means            4    47.799 4042.5 1539.5
## - parent_educ:reading_score               5    61.928 4056.7 1539.5
## - ethnic_group:is_first_child             4    52.682 4047.4 1540.2
## - parent_educ:transport_means             5    66.600 4061.3 1540.2
## - lunch_type:is_first_child               1    12.630 4007.4 1540.3
## - transport_means:wkly_study_hours        2    26.387 4021.1 1540.3
## <none>                                                3994.7 1540.4
## - lunch_type:math_score                   1    15.303 4010.0 1540.7
## - gender:ethnic_group                     4    58.078 4052.8 1541.0
## - parent_educ:math_score                  5    71.907 4066.6 1541.0
## - test_prep:is_first_child                1    18.098 4012.8 1541.1
## - practice_sport:math_score               2    31.895 4026.6 1541.1
## - gender:math_score                       1    19.962 4014.7 1541.4
## - parent_educ:lunch_type                  5    75.243 4070.0 1541.5
## - practice_sport:reading_score            2    38.767 4033.5 1542.1
## - ethnic_group:math_score                 4    69.183 4063.9 1542.6
## - practice_sport:is_first_child           2    41.813 4036.5 1542.6
## - test_prep:practice_sport                2    42.260 4037.0 1542.7
## - test_prep:transport_means               1    33.244 4028.0 1543.3
## + parent_educ:parent_marital_status      13   147.779 3846.9 1544.2
## + gender:practice_sport                   2     0.663 3994.1 1544.3
## - test_prep:parent_marital_status         3    68.126 4062.8 1544.4
## - gender:reading_score                    1    41.040 4035.8 1544.5
## - parent_marital_status:wkly_study_hours  6   111.050 4105.8 1544.6
## + parent_marital_status:is_first_child    3     4.440 3990.3 1545.8
## + gender:parent_educ                      5    26.495 3968.2 1546.5
## + parent_marital_status:practice_sport    5    25.409 3969.3 1546.7
## + practice_sport:wkly_study_hours         4    11.502 3983.2 1546.7
## + ethnic_group:reading_score              4     7.731 3987.0 1547.3
## - ethnic_group:wkly_study_hours           8   161.021 4155.7 1547.8
## - ethnic_group:lunch_type                 4   110.804 4105.5 1548.6
## - parent_educ:practice_sport             10   199.101 4193.8 1549.1
## - math_score:reading_score                1    76.170 4070.9 1549.6
## + parent_educ:wkly_study_hours           10    61.034 3933.7 1551.3
## - parent_educ:is_first_child              5   183.596 4178.3 1557.0
## 
## Step:  AIC=1535.51
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + gender:math_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:math_score + 
##     parent_marital_status:reading_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_marital_status:transport_means   3    13.099 4042.3 1531.4
## - ethnic_group:test_prep                  4    29.957 4059.2 1531.9
## - practice_sport:transport_means          2     6.423 4035.6 1532.5
## - gender:wkly_study_hours                 2     6.484 4035.7 1532.5
## - is_first_child:wkly_study_hours         2     6.642 4035.8 1532.5
## - test_prep:wkly_study_hours              2     6.717 4035.9 1532.5
## - lunch_type:wkly_study_hours             2     8.458 4037.7 1532.8
## - parent_marital_status:math_score        3    24.009 4053.2 1533.0
## - wkly_study_hours:math_score             2    11.932 4041.1 1533.2
## - ethnic_group:parent_educ               20   266.752 4296.0 1533.3
## - lunch_type:parent_marital_status        3    26.887 4056.1 1533.4
## - lunch_type:transport_means              1     0.037 4029.2 1533.5
## - is_first_child:transport_means          1     0.199 4029.4 1533.5
## - is_first_child:reading_score            1     0.303 4029.5 1533.5
## - gender:transport_means                  1     0.411 4029.6 1533.6
## - test_prep:reading_score                 1     0.412 4029.6 1533.6
## - gender:test_prep                        1     0.429 4029.6 1533.6
## - lunch_type:test_prep                    1     0.430 4029.6 1533.6
## - test_prep:math_score                    1     0.551 4029.8 1533.6
## - parent_marital_status:reading_score     3    28.042 4057.2 1533.6
## - gender:lunch_type                       1     0.738 4029.9 1533.6
## - lunch_type:practice_sport               2    15.473 4044.7 1533.8
## - gender:parent_marital_status            3    29.609 4058.8 1533.8
## - transport_means:reading_score           1     3.040 4032.2 1534.0
## - wkly_study_hours:reading_score          2    17.726 4046.9 1534.1
## - lunch_type:reading_score                1     4.090 4033.3 1534.1
## - is_first_child:math_score               1     4.182 4033.4 1534.1
## - gender:is_first_child                   1     4.820 4034.0 1534.2
## - parent_educ:reading_score               5    60.012 4089.2 1534.2
## - ethnic_group:transport_means            4    47.080 4076.3 1534.4
## - transport_means:math_score              1     6.530 4035.7 1534.5
## - ethnic_group:practice_sport             8   104.117 4133.3 1534.6
## - ethnic_group:parent_marital_status     11   148.251 4177.5 1534.8
## - parent_educ:transport_means             5    67.389 4096.6 1535.3
## - lunch_type:is_first_child               1    12.329 4041.5 1535.3
## <none>                                                4029.2 1535.5
## - ethnic_group:is_first_child             4    55.136 4084.3 1535.5
## - transport_means:wkly_study_hours        2    28.271 4057.5 1535.6
## - lunch_type:math_score                   1    14.553 4043.8 1535.6
## - gender:ethnic_group                     4    56.172 4085.4 1535.7
## - test_prep:is_first_child                1    19.882 4049.1 1536.4
## - practice_sport:math_score               2    33.970 4063.2 1536.5
## - gender:math_score                       1    20.739 4049.9 1536.5
## - ethnic_group:math_score                 4    65.479 4094.7 1537.0
## - parent_educ:math_score                  5    79.448 4108.6 1537.0
## - parent_educ:lunch_type                  5    82.228 4111.4 1537.4
## - practice_sport:is_first_child           2    43.893 4073.1 1537.9
## - practice_sport:reading_score            2    44.302 4073.5 1538.0
## - test_prep:transport_means               1    31.485 4060.7 1538.1
## - test_prep:practice_sport                2    47.537 4076.7 1538.4
## - test_prep:parent_marital_status         3    63.701 4092.9 1538.8
## - gender:reading_score                    1    39.019 4068.2 1539.2
## + gender:practice_sport                   2     0.313 4028.9 1539.5
## - parent_marital_status:wkly_study_hours  6   110.748 4139.9 1539.5
## + parent_educ:test_prep                   5    34.478 3994.7 1540.4
## + parent_marital_status:is_first_child    3     4.612 4024.6 1540.8
## + practice_sport:wkly_study_hours         4    12.948 4016.3 1541.6
## + parent_marital_status:practice_sport    5    21.986 4007.2 1542.3
## + ethnic_group:reading_score              4     7.461 4021.7 1542.4
## + parent_educ:parent_marital_status      13   127.454 3901.7 1542.5
## + gender:parent_educ                      5    19.881 4009.3 1542.6
## - ethnic_group:wkly_study_hours           8   163.150 4192.3 1542.9
## - parent_educ:practice_sport             10   196.176 4225.4 1543.6
## - math_score:reading_score                1    75.442 4104.6 1544.5
## - ethnic_group:lunch_type                 4   117.548 4146.7 1544.5
## + parent_educ:wkly_study_hours           10    61.686 3967.5 1546.4
## - parent_educ:is_first_child              5   179.211 4208.4 1551.2
## 
## Step:  AIC=1531.42
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + gender:math_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:math_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - is_first_child:wkly_study_hours         2     4.289 4046.6 1528.0
## - parent_marital_status:math_score        3    18.568 4060.9 1528.1
## - gender:wkly_study_hours                 2     5.959 4048.3 1528.3
## - ethnic_group:test_prep                  4    35.042 4077.3 1528.5
## - practice_sport:transport_means          2     7.582 4049.9 1528.5
## - test_prep:wkly_study_hours              2     8.091 4050.4 1528.6
## - lunch_type:wkly_study_hours             2     8.671 4051.0 1528.7
## - parent_marital_status:reading_score     3    22.745 4065.0 1528.7
## - lunch_type:parent_marital_status        3    22.856 4065.2 1528.8
## - wkly_study_hours:math_score             2    10.374 4052.7 1528.9
## - ethnic_group:parent_educ               20   266.664 4309.0 1529.1
## - lunch_type:transport_means              1     0.008 4042.3 1529.4
## - gender:transport_means                  1     0.302 4042.6 1529.5
## - is_first_child:reading_score            1     0.336 4042.6 1529.5
## - is_first_child:transport_means          1     0.357 4042.7 1529.5
## - test_prep:reading_score                 1     0.513 4042.8 1529.5
## - lunch_type:test_prep                    1     0.589 4042.9 1529.5
## - gender:test_prep                        1     0.696 4043.0 1529.5
## - gender:parent_marital_status            3    28.244 4070.5 1529.5
## - test_prep:math_score                    1     0.818 4043.1 1529.5
## - gender:lunch_type                       1     1.006 4043.3 1529.6
## - parent_educ:reading_score               5    57.074 4099.4 1529.7
## - lunch_type:practice_sport               2    15.986 4058.3 1529.8
## - wkly_study_hours:reading_score          2    16.460 4058.8 1529.8
## - transport_means:reading_score           1     2.838 4045.1 1529.8
## - lunch_type:reading_score                1     4.087 4046.4 1530.0
## - is_first_child:math_score               1     4.185 4046.5 1530.0
## - ethnic_group:practice_sport             8   101.856 4144.2 1530.1
## - gender:is_first_child                   1     4.916 4047.2 1530.1
## - ethnic_group:transport_means            4    46.801 4089.1 1530.2
## - ethnic_group:parent_marital_status     11   145.809 4188.1 1530.3
## - transport_means:math_score              1     6.456 4048.8 1530.4
## - lunch_type:is_first_child               1    11.845 4054.1 1531.2
## - parent_educ:transport_means             5    67.513 4109.8 1531.2
## <none>                                                4042.3 1531.4
## - lunch_type:math_score                   1    13.968 4056.3 1531.5
## - transport_means:wkly_study_hours        2    28.511 4070.8 1531.6
## - practice_sport:math_score               2    31.176 4073.5 1532.0
## - gender:math_score                       1    17.692 4060.0 1532.0
## - gender:ethnic_group                     4    60.187 4102.5 1532.1
## - ethnic_group:is_first_child             4    60.284 4102.6 1532.2
## - test_prep:is_first_child                1    20.279 4062.6 1532.4
## - parent_educ:math_score                  5    77.463 4119.8 1532.6
## - parent_educ:lunch_type                  5    79.757 4122.1 1533.0
## - test_prep:transport_means               1    26.682 4069.0 1533.3
## - ethnic_group:math_score                 4    69.118 4111.4 1533.4
## - practice_sport:reading_score            2    42.942 4085.2 1533.7
## - practice_sport:is_first_child           2    43.391 4085.7 1533.7
## - test_prep:practice_sport                2    49.086 4091.4 1534.5
## - gender:reading_score                    1    37.057 4079.4 1534.8
## - parent_marital_status:wkly_study_hours  6   108.596 4150.9 1535.1
## - test_prep:parent_marital_status         3    68.244 4110.5 1535.3
## + gender:practice_sport                   2     0.218 4042.1 1535.4
## + parent_marital_status:transport_means   3    13.099 4029.2 1535.5
## + parent_educ:test_prep                   5    35.189 4007.1 1536.3
## + parent_marital_status:is_first_child    3     7.416 4034.9 1536.3
## + practice_sport:wkly_study_hours         4    13.349 4029.0 1537.5
## + parent_marital_status:practice_sport    5    24.657 4017.6 1537.8
## + ethnic_group:reading_score              4     8.194 4034.1 1538.2
## + gender:parent_educ                      5    18.451 4023.8 1538.7
## - parent_educ:practice_sport             10   192.112 4234.4 1538.8
## - ethnic_group:wkly_study_hours           8   165.310 4207.6 1539.1
## + parent_educ:parent_marital_status      14   131.161 3911.1 1540.0
## - ethnic_group:lunch_type                 4   117.113 4159.4 1540.3
## - math_score:reading_score                1    76.701 4119.0 1540.5
## + parent_educ:wkly_study_hours           10    60.928 3981.4 1542.5
## - parent_educ:is_first_child              5   196.733 4239.0 1549.5
## 
## Step:  AIC=1528.05
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + gender:math_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:math_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_marital_status:math_score        3    16.905 4063.5 1524.5
## - gender:wkly_study_hours                 2     5.613 4052.2 1524.9
## - test_prep:wkly_study_hours              2     7.030 4053.6 1525.1
## - parent_marital_status:reading_score     3    20.971 4067.6 1525.1
## - ethnic_group:test_prep                  4    34.823 4081.4 1525.1
## - practice_sport:transport_means          2     7.866 4054.5 1525.2
## - lunch_type:wkly_study_hours             2     9.098 4055.7 1525.4
## - lunch_type:parent_marital_status        3    23.402 4070.0 1525.5
## - wkly_study_hours:math_score             2    10.191 4056.8 1525.5
## - ethnic_group:parent_educ               20   266.160 4312.7 1525.6
## - gender:parent_marital_status            3    26.455 4073.0 1525.9
## - lunch_type:transport_means              1     0.005 4046.6 1526.0
## - is_first_child:reading_score            1     0.149 4046.7 1526.1
## - gender:transport_means                  1     0.300 4046.9 1526.1
## - is_first_child:transport_means          1     0.487 4047.1 1526.1
## - test_prep:reading_score                 1     0.508 4047.1 1526.1
## - gender:test_prep                        1     0.654 4047.2 1526.1
## - lunch_type:test_prep                    1     0.709 4047.3 1526.2
## - test_prep:math_score                    1     0.724 4047.3 1526.2
## - lunch_type:practice_sport               2    14.526 4061.1 1526.2
## - parent_educ:reading_score               5    56.397 4103.0 1526.2
## - gender:lunch_type                       1     1.214 4047.8 1526.2
## - wkly_study_hours:reading_score          2    15.700 4062.3 1526.3
## - transport_means:reading_score           1     2.882 4049.5 1526.5
## - is_first_child:math_score               1     3.031 4049.6 1526.5
## - gender:is_first_child                   1     3.819 4050.4 1526.6
## - lunch_type:reading_score                1     4.296 4050.9 1526.7
## - ethnic_group:practice_sport             8   101.764 4148.4 1526.7
## - ethnic_group:transport_means            4    47.072 4093.7 1526.9
## - transport_means:math_score              1     6.389 4053.0 1527.0
## - ethnic_group:parent_marital_status     11   150.842 4197.4 1527.6
## - lunch_type:is_first_child               1    11.722 4058.3 1527.8
## - parent_educ:transport_means             5    69.143 4115.7 1528.0
## <none>                                                4046.6 1528.0
## - lunch_type:math_score                   1    14.188 4060.8 1528.1
## - transport_means:wkly_study_hours        2    29.647 4076.2 1528.4
## - gender:math_score                       1    17.025 4063.6 1528.5
## - practice_sport:math_score               2    31.808 4078.4 1528.7
## - ethnic_group:is_first_child             4    59.782 4106.4 1528.7
## - parent_educ:math_score                  5    75.889 4122.5 1529.0
## - gender:ethnic_group                     4    62.431 4109.0 1529.1
## - test_prep:is_first_child                1    22.907 4069.5 1529.4
## - test_prep:transport_means               1    25.455 4072.0 1529.8
## - ethnic_group:math_score                 4    69.141 4115.7 1530.0
## - parent_educ:lunch_type                  5    83.150 4129.7 1530.0
## - practice_sport:is_first_child           2    43.979 4090.6 1530.4
## - practice_sport:reading_score            2    45.410 4092.0 1530.6
## - parent_marital_status:wkly_study_hours  6   105.886 4152.5 1531.3
## - test_prep:practice_sport                2    50.445 4097.0 1531.4
## - gender:reading_score                    1    36.616 4083.2 1531.4
## + is_first_child:wkly_study_hours         2     4.289 4042.3 1531.4
## + gender:practice_sport                   2     0.120 4046.5 1532.0
## - test_prep:parent_marital_status         3    69.789 4116.4 1532.1
## + parent_marital_status:transport_means   3    10.746 4035.8 1532.5
## + parent_marital_status:is_first_child    3     7.199 4039.4 1533.0
## + parent_educ:test_prep                   5    31.560 4015.0 1533.4
## + practice_sport:wkly_study_hours         4    13.027 4033.6 1534.2
## + parent_marital_status:practice_sport    5    22.611 4024.0 1534.7
## + ethnic_group:reading_score              4     8.187 4038.4 1534.8
## - parent_educ:practice_sport             10   191.112 4237.7 1535.3
## + gender:parent_educ                      5    17.816 4028.8 1535.5
## - ethnic_group:wkly_study_hours           8   164.190 4210.8 1535.5
## - ethnic_group:lunch_type                 4   117.478 4164.1 1536.9
## - math_score:reading_score                1    75.541 4122.1 1537.0
## + parent_educ:parent_marital_status      14   127.310 3919.3 1537.2
## + parent_educ:wkly_study_hours           10    59.075 3987.5 1539.4
## - parent_educ:is_first_child              5   197.175 4243.8 1546.1
## 
## Step:  AIC=1524.51
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + gender:math_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:reading_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_marital_status:reading_score     3     8.016 4071.5 1519.7
## - gender:parent_marital_status            3    15.793 4079.3 1520.8
## - gender:wkly_study_hours                 2     6.548 4070.0 1521.5
## - ethnic_group:test_prep                  4    34.618 4098.1 1521.5
## - lunch_type:wkly_study_hours             2     7.806 4071.3 1521.6
## - practice_sport:transport_means          2     7.846 4071.3 1521.7
## - test_prep:wkly_study_hours              2     8.694 4072.2 1521.8
## - wkly_study_hours:math_score             2     8.838 4072.3 1521.8
## - ethnic_group:practice_sport             8    96.102 4159.6 1522.3
## - lunch_type:practice_sport               2    13.480 4077.0 1522.5
## - lunch_type:transport_means              1     0.000 4063.5 1522.5
## - is_first_child:reading_score            1     0.002 4063.5 1522.5
## - gender:transport_means                  1     0.026 4063.5 1522.5
## - gender:test_prep                        1     0.356 4063.8 1522.6
## - test_prep:reading_score                 1     0.357 4063.9 1522.6
## - test_prep:math_score                    1     0.398 4063.9 1522.6
## - is_first_child:transport_means          1     0.659 4064.2 1522.6
## - wkly_study_hours:reading_score          2    14.737 4078.2 1522.6
## - lunch_type:test_prep                    1     1.136 4064.6 1522.7
## - gender:lunch_type                       1     1.802 4065.3 1522.8
## - is_first_child:math_score               1     1.883 4065.4 1522.8
## - transport_means:reading_score           1     2.159 4065.7 1522.8
## - gender:is_first_child                   1     2.799 4066.3 1522.9
## - ethnic_group:parent_educ               20   273.729 4337.2 1523.0
## - parent_educ:reading_score               5    59.536 4123.0 1523.1
## - lunch_type:reading_score                1     4.466 4068.0 1523.2
## - ethnic_group:transport_means            4    47.199 4110.7 1523.3
## - transport_means:math_score              1     7.052 4070.5 1523.5
## - lunch_type:is_first_child               1     9.834 4073.3 1523.9
## - parent_educ:transport_means             5    67.293 4130.8 1524.2
## - gender:math_score                       1    12.505 4076.0 1524.3
## <none>                                                4063.5 1524.5
## - lunch_type:math_score                   1    14.283 4077.8 1524.6
## - ethnic_group:is_first_child             4    56.295 4119.8 1524.6
## - lunch_type:parent_marital_status        3    42.922 4106.4 1524.7
## - practice_sport:math_score               2    32.023 4095.5 1525.1
## - transport_means:wkly_study_hours        2    32.797 4096.3 1525.2
## - parent_educ:math_score                  5    75.225 4138.7 1525.3
## - test_prep:is_first_child                1    23.691 4087.2 1525.9
## - test_prep:transport_means               1    24.426 4087.9 1526.0
## - gender:ethnic_group                     4    66.343 4129.8 1526.1
## - ethnic_group:parent_marital_status     11   166.297 4229.8 1526.2
## - parent_educ:lunch_type                  5    81.915 4145.4 1526.3
## - practice_sport:is_first_child           2    43.140 4106.6 1526.7
## - practice_sport:reading_score            2    44.198 4107.7 1526.9
## - parent_marital_status:wkly_study_hours  6   100.881 4164.4 1527.0
## - gender:reading_score                    1    31.363 4094.9 1527.0
## - test_prep:practice_sport                2    49.638 4113.1 1527.7
## - ethnic_group:math_score                 4    77.696 4141.2 1527.7
## + parent_marital_status:math_score        3    16.905 4046.6 1528.0
## + is_first_child:wkly_study_hours         2     2.626 4060.9 1528.1
## + gender:practice_sport                   2     0.135 4063.4 1528.5
## - test_prep:parent_marital_status         3    69.990 4133.5 1528.6
## + parent_marital_status:is_first_child    3     6.727 4056.8 1529.5
## + parent_marital_status:transport_means   3     6.389 4057.1 1529.6
## + parent_educ:test_prep                   5    33.306 4030.2 1529.7
## + practice_sport:wkly_study_hours         4    12.556 4050.9 1530.7
## + parent_marital_status:practice_sport    5    25.021 4038.5 1530.9
## + ethnic_group:reading_score              4    11.101 4052.4 1530.9
## + gender:parent_educ                      5    18.043 4045.5 1531.9
## - parent_educ:practice_sport             10   194.319 4257.8 1532.1
## - ethnic_group:wkly_study_hours           8   165.976 4229.5 1532.1
## - math_score:reading_score                1    76.473 4140.0 1533.5
## - ethnic_group:lunch_type                 4   121.687 4185.2 1533.9
## + parent_educ:wkly_study_hours           10    58.412 4005.1 1536.0
## + parent_educ:parent_marital_status      15   120.285 3943.2 1536.8
## - parent_educ:is_first_child              5   193.510 4257.0 1542.0
## 
## Step:  AIC=1519.67
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + gender:math_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:parent_marital_status            3    14.575 4086.1 1515.8
## - gender:wkly_study_hours                 2     6.006 4077.5 1516.5
## - lunch_type:wkly_study_hours             2     7.571 4079.1 1516.8
## - practice_sport:transport_means          2     7.691 4079.2 1516.8
## - test_prep:wkly_study_hours              2     7.878 4079.4 1516.8
## - ethnic_group:test_prep                  4    35.765 4107.3 1516.8
## - wkly_study_hours:math_score             2     8.990 4080.5 1517.0
## - ethnic_group:practice_sport             8    95.780 4167.3 1517.4
## - ethnic_group:parent_educ               20   270.182 4341.7 1517.6
## - lunch_type:practice_sport               2    13.520 4085.0 1517.6
## - gender:transport_means                  1     0.000 4071.5 1517.7
## - lunch_type:transport_means              1     0.002 4071.5 1517.7
## - is_first_child:reading_score            1     0.036 4071.5 1517.7
## - gender:test_prep                        1     0.463 4072.0 1517.7
## - test_prep:reading_score                 1     0.624 4072.1 1517.8
## - test_prep:math_score                    1     0.746 4072.3 1517.8
## - wkly_study_hours:reading_score          2    14.725 4086.2 1517.8
## - is_first_child:transport_means          1     0.931 4072.4 1517.8
## - lunch_type:test_prep                    1     1.016 4072.5 1517.8
## - is_first_child:math_score               1     1.245 4072.8 1517.8
## - parent_educ:reading_score               5    57.213 4128.7 1517.9
## - gender:lunch_type                       1     1.619 4073.1 1517.9
## - transport_means:reading_score           1     1.651 4073.2 1517.9
## - gender:is_first_child                   1     2.094 4073.6 1518.0
## - lunch_type:reading_score                1     4.457 4076.0 1518.3
## - ethnic_group:transport_means            4    46.758 4118.3 1518.4
## - transport_means:math_score              1     7.658 4079.2 1518.8
## - lunch_type:is_first_child               1    10.204 4081.7 1519.2
## - parent_educ:transport_means             5    67.051 4138.6 1519.3
## - ethnic_group:is_first_child             4    54.591 4126.1 1519.5
## <none>                                                4071.5 1519.7
## - gender:math_score                       1    14.695 4086.2 1519.8
## - lunch_type:math_score                   1    14.958 4086.5 1519.8
## - lunch_type:parent_marital_status        3    43.116 4114.6 1519.9
## - transport_means:wkly_study_hours        2    32.982 4104.5 1520.4
## - parent_educ:math_score                  5    75.385 4146.9 1520.5
## - ethnic_group:parent_marital_status     11   160.868 4232.4 1520.5
## - practice_sport:math_score               2    33.881 4105.4 1520.6
## - test_prep:transport_means               1    23.189 4094.7 1521.0
## - gender:ethnic_group                     4    66.249 4137.8 1521.2
## - test_prep:is_first_child                1    26.218 4097.7 1521.5
## - parent_educ:lunch_type                  5    83.672 4155.2 1521.7
## - ethnic_group:math_score                 4    74.094 4145.6 1522.3
## - gender:reading_score                    1    33.499 4105.0 1522.5
## - parent_marital_status:wkly_study_hours  6   103.837 4175.3 1522.5
## - practice_sport:reading_score            2    47.660 4119.2 1522.5
## - practice_sport:is_first_child           2    48.697 4120.2 1522.7
## - test_prep:practice_sport                2    51.071 4122.6 1523.0
## + is_first_child:wkly_study_hours         2     2.605 4068.9 1523.3
## + gender:practice_sport                   2     0.129 4071.4 1523.7
## - test_prep:parent_marital_status         3    73.688 4145.2 1524.2
## + parent_marital_status:is_first_child    3     8.072 4063.4 1524.5
## + parent_educ:test_prep                   5    35.478 4036.0 1524.5
## + parent_marital_status:reading_score     3     8.016 4063.5 1524.5
## + parent_marital_status:transport_means   3     7.020 4064.5 1524.7
## + parent_marital_status:math_score        3     3.950 4067.6 1525.1
## + parent_marital_status:practice_sport    5    27.303 4044.2 1525.7
## + ethnic_group:reading_score              4    11.931 4059.6 1525.9
## + practice_sport:wkly_study_hours         4    11.918 4059.6 1525.9
## - ethnic_group:wkly_study_hours           8   161.810 4233.3 1526.7
## + gender:parent_educ                      5    18.003 4053.5 1527.1
## - parent_educ:practice_sport             10   196.144 4267.7 1527.4
## - ethnic_group:lunch_type                 4   124.017 4195.5 1529.4
## - math_score:reading_score                1    87.496 4159.0 1530.2
## + parent_educ:wkly_study_hours           10    59.089 4012.4 1531.0
## + parent_educ:parent_marital_status      15   111.411 3960.1 1533.3
## - parent_educ:is_first_child              5   192.738 4264.2 1537.0
## 
## Step:  AIC=1515.78
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:math_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:wkly_study_hours                 2     5.512 4091.6 1512.6
## - lunch_type:wkly_study_hours             2     5.762 4091.8 1512.6
## - practice_sport:transport_means          2     7.031 4093.1 1512.8
## - test_prep:wkly_study_hours              2     7.301 4093.4 1512.8
## - wkly_study_hours:math_score             2     7.679 4093.8 1512.9
## - ethnic_group:parent_educ               20   268.754 4354.8 1513.4
## - lunch_type:practice_sport               2    13.035 4099.1 1513.7
## - wkly_study_hours:reading_score          2    13.656 4099.7 1513.8
## - gender:transport_means                  1     0.046 4086.1 1513.8
## - is_first_child:reading_score            1     0.053 4086.1 1513.8
## - lunch_type:transport_means              1     0.091 4086.2 1513.8
## - ethnic_group:test_prep                  4    41.971 4128.1 1513.8
## - gender:test_prep                        1     0.696 4086.8 1513.9
## - test_prep:reading_score                 1     0.722 4086.8 1513.9
## - lunch_type:test_prep                    1     0.895 4087.0 1513.9
## - test_prep:math_score                    1     0.903 4087.0 1513.9
## - is_first_child:math_score               1     1.026 4087.1 1513.9
## - is_first_child:transport_means          1     1.084 4087.2 1513.9
## - transport_means:reading_score           1     1.171 4087.3 1514.0
## - gender:lunch_type                       1     1.502 4087.6 1514.0
## - gender:is_first_child                   1     1.920 4088.0 1514.1
## - parent_educ:reading_score               5    58.777 4144.9 1514.2
## - ethnic_group:practice_sport             8   102.321 4188.4 1514.4
## - lunch_type:reading_score                1     4.119 4090.2 1514.4
## - ethnic_group:transport_means            4    50.821 4136.9 1515.1
## - transport_means:math_score              1     9.973 4096.1 1515.2
## - ethnic_group:parent_marital_status     11   152.415 4238.5 1515.4
## - lunch_type:is_first_child               1    11.454 4097.5 1515.4
## - parent_educ:transport_means             5    67.633 4153.7 1515.5
## - ethnic_group:is_first_child             4    54.067 4140.2 1515.5
## - gender:math_score                       1    13.595 4099.7 1515.7
## <none>                                                4086.1 1515.8
## - lunch_type:parent_marital_status        3    42.590 4128.7 1515.9
## - lunch_type:math_score                   1    15.038 4101.1 1516.0
## - parent_educ:math_score                  5    73.970 4160.1 1516.4
## - transport_means:wkly_study_hours        2    32.491 4118.6 1516.5
## - practice_sport:math_score               2    36.233 4122.3 1517.0
## - test_prep:transport_means               1    22.978 4109.1 1517.1
## - gender:ethnic_group                     4    67.060 4153.1 1517.4
## - test_prep:is_first_child                1    26.077 4112.2 1517.5
## - parent_educ:lunch_type                  5    82.467 4168.6 1517.6
## - gender:reading_score                    1    30.146 4116.2 1518.1
## - parent_marital_status:wkly_study_hours  6   101.482 4187.6 1518.2
## - practice_sport:reading_score            2    46.237 4132.3 1518.4
## - practice_sport:is_first_child           2    47.004 4133.1 1518.5
## - ethnic_group:math_score                 4    77.107 4163.2 1518.8
## - test_prep:practice_sport                2    49.227 4135.3 1518.8
## + is_first_child:wkly_study_hours         2     2.178 4083.9 1519.5
## + gender:parent_marital_status            3    14.575 4071.5 1519.7
## + gender:practice_sport                   2     0.236 4085.8 1519.8
## + parent_marital_status:is_first_child    3     7.843 4078.2 1520.7
## + parent_marital_status:transport_means   3     7.760 4078.3 1520.7
## + parent_marital_status:reading_score     3     6.798 4079.3 1520.8
## + parent_educ:test_prep                   5    33.440 4052.6 1520.9
## - test_prep:parent_marital_status         3    80.664 4166.7 1521.3
## + parent_marital_status:math_score        3     2.616 4083.5 1521.4
## + parent_marital_status:practice_sport    5    26.833 4059.3 1521.9
## + ethnic_group:reading_score              4    12.980 4073.1 1521.9
## + practice_sport:wkly_study_hours         4    11.957 4074.1 1522.0
## + gender:parent_educ                      5    18.543 4067.5 1523.1
## - ethnic_group:wkly_study_hours           8   166.181 4252.3 1523.3
## - parent_educ:practice_sport             10   197.482 4283.6 1523.6
## - ethnic_group:lunch_type                 4   120.081 4206.2 1524.9
## + parent_educ:wkly_study_hours           10    61.936 4024.1 1526.8
## - math_score:reading_score                1    92.142 4178.2 1526.9
## + parent_educ:parent_marital_status      15   117.817 3968.3 1528.5
## - parent_educ:is_first_child              5   202.069 4288.2 1534.3
## 
## Step:  AIC=1512.58
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:wkly_study_hours             2     5.815 4097.4 1509.4
## - practice_sport:transport_means          2     6.684 4098.3 1509.5
## - test_prep:wkly_study_hours              2     8.558 4100.2 1509.8
## - wkly_study_hours:math_score             2     8.803 4100.4 1509.8
## - ethnic_group:parent_educ               20   268.329 4359.9 1510.0
## - lunch_type:practice_sport               2    12.525 4104.1 1510.4
## - gender:transport_means                  1     0.130 4091.7 1510.6
## - lunch_type:transport_means              1     0.194 4091.8 1510.6
## - is_first_child:reading_score            1     0.197 4091.8 1510.6
## - gender:test_prep                        1     0.616 4092.2 1510.7
## - lunch_type:test_prep                    1     0.706 4092.3 1510.7
## - is_first_child:math_score               1     0.735 4092.3 1510.7
## - test_prep:reading_score                 1     0.751 4092.3 1510.7
## - test_prep:math_score                    1     0.881 4092.5 1510.7
## - transport_means:reading_score           1     0.975 4092.6 1510.7
## - is_first_child:transport_means          1     1.052 4092.6 1510.7
## - gender:lunch_type                       1     1.248 4092.8 1510.8
## - gender:is_first_child                   1     1.383 4093.0 1510.8
## - ethnic_group:test_prep                  4    43.574 4135.2 1510.8
## - parent_educ:reading_score               5    59.416 4151.0 1511.1
## - wkly_study_hours:reading_score          2    18.133 4109.7 1511.2
## - lunch_type:reading_score                1     4.230 4095.8 1511.2
## - ethnic_group:practice_sport             8   103.982 4195.6 1511.4
## - ethnic_group:transport_means            4    51.106 4142.7 1511.9
## - lunch_type:is_first_child               1    10.887 4102.5 1512.1
## - transport_means:math_score              1    11.244 4102.8 1512.2
## - parent_educ:transport_means             5    67.329 4158.9 1512.2
## - lunch_type:parent_marital_status        3    41.514 4133.1 1512.5
## - ethnic_group:is_first_child             4    55.596 4147.2 1512.5
## - ethnic_group:parent_marital_status     11   155.240 4246.8 1512.5
## <none>                                                4091.6 1512.6
## - lunch_type:math_score                   1    15.448 4107.0 1512.8
## - gender:math_score                       1    16.544 4108.1 1513.0
## - transport_means:wkly_study_hours        2    34.330 4125.9 1513.5
## - parent_educ:math_score                  5    77.091 4168.7 1513.6
## - practice_sport:math_score               2    35.312 4126.9 1513.7
## - gender:ethnic_group                     4    64.232 4155.8 1513.8
## - test_prep:transport_means               1    22.453 4114.0 1513.8
## - parent_educ:lunch_type                  5    79.920 4171.5 1514.0
## - test_prep:is_first_child                1    28.317 4119.9 1514.6
## - practice_sport:reading_score            2    44.650 4136.2 1515.0
## - ethnic_group:math_score                 4    75.126 4166.7 1515.3
## - gender:reading_score                    1    33.089 4124.7 1515.3
## - test_prep:practice_sport                2    47.506 4139.1 1515.4
## - parent_marital_status:wkly_study_hours  6   104.758 4196.4 1515.5
## - practice_sport:is_first_child           2    48.452 4140.0 1515.5
## + gender:wkly_study_hours                 2     5.512 4086.1 1515.8
## + is_first_child:wkly_study_hours         2     1.855 4089.7 1516.3
## + gender:practice_sport                   2     0.546 4091.1 1516.5
## + gender:parent_marital_status            3    14.081 4077.5 1516.5
## + parent_marital_status:is_first_child    3     7.848 4083.7 1517.4
## + parent_marital_status:transport_means   3     7.270 4084.3 1517.5
## + parent_marital_status:reading_score     3     6.400 4085.2 1517.7
## + parent_educ:test_prep                   5    33.422 4058.2 1517.7
## + parent_marital_status:math_score        3     2.657 4088.9 1518.2
## - test_prep:parent_marital_status         3    81.548 4173.1 1518.2
## + parent_marital_status:practice_sport    5    27.453 4064.1 1518.6
## + practice_sport:wkly_study_hours         4    12.928 4078.7 1518.7
## + ethnic_group:reading_score              4    11.435 4080.2 1518.9
## + gender:parent_educ                      5    19.118 4072.5 1519.8
## - ethnic_group:wkly_study_hours           8   164.492 4256.1 1519.8
## - parent_educ:practice_sport             10   198.898 4290.5 1520.6
## - ethnic_group:lunch_type                 4   123.472 4215.1 1522.1
## - math_score:reading_score                1    91.900 4183.5 1523.7
## + parent_educ:wkly_study_hours           10    58.512 4033.1 1524.1
## + parent_educ:parent_marital_status      15   116.282 3975.3 1525.6
## - parent_educ:is_first_child              5   197.160 4288.8 1530.3
## 
## Step:  AIC=1509.41
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:parent_educ               20   263.576 4361.0 1506.2
## - wkly_study_hours:math_score             2     5.603 4103.0 1506.2
## - practice_sport:transport_means          2     7.004 4104.4 1506.4
## - test_prep:wkly_study_hours              2     9.331 4106.7 1506.8
## - lunch_type:practice_sport               2    13.567 4111.0 1507.4
## - gender:transport_means                  1     0.139 4097.6 1507.4
## - is_first_child:reading_score            1     0.166 4097.6 1507.4
## - lunch_type:transport_means              1     0.310 4097.7 1507.5
## - lunch_type:test_prep                    1     0.599 4098.0 1507.5
## - gender:test_prep                        1     0.637 4098.0 1507.5
## - test_prep:reading_score                 1     0.654 4098.1 1507.5
## - is_first_child:math_score               1     0.754 4098.2 1507.5
## - is_first_child:transport_means          1     0.796 4098.2 1507.5
## - test_prep:math_score                    1     0.848 4098.3 1507.5
## - transport_means:reading_score           1     0.859 4098.3 1507.5
## - gender:lunch_type                       1     0.903 4098.3 1507.5
## - gender:is_first_child                   1     1.264 4098.7 1507.6
## - ethnic_group:test_prep                  4    44.930 4142.3 1507.8
## - parent_educ:reading_score               5    59.115 4156.5 1507.9
## - lunch_type:reading_score                1     3.160 4100.6 1507.9
## - wkly_study_hours:reading_score          2    17.654 4115.1 1508.0
## - ethnic_group:practice_sport             8   103.007 4200.4 1508.1
## - parent_educ:transport_means             5    65.294 4162.7 1508.7
## - lunch_type:is_first_child               1    11.117 4108.5 1509.0
## - ethnic_group:transport_means            4    53.291 4150.7 1509.0
## - transport_means:math_score              1    11.931 4109.3 1509.1
## - ethnic_group:is_first_child             4    54.719 4152.1 1509.2
## - lunch_type:math_score                   1    13.855 4111.3 1509.4
## <none>                                                4097.4 1509.4
## - lunch_type:parent_marital_status        3    43.170 4140.6 1509.6
## - ethnic_group:parent_marital_status     11   157.000 4254.4 1509.6
## - gender:math_score                       1    17.375 4114.8 1509.9
## - parent_educ:math_score                  5    75.257 4172.7 1510.2
## - transport_means:wkly_study_hours        2    34.080 4131.5 1510.3
## - practice_sport:math_score               2    34.227 4131.6 1510.3
## - gender:ethnic_group                     4    65.052 4162.5 1510.7
## - parent_educ:lunch_type                  5    79.850 4177.3 1510.8
## - test_prep:transport_means               1    25.068 4122.5 1511.0
## - practice_sport:reading_score            2    43.006 4140.4 1511.6
## - test_prep:is_first_child                1    29.814 4127.2 1511.7
## - parent_marital_status:wkly_study_hours  6   102.182 4199.6 1512.0
## - test_prep:practice_sport                2    46.263 4143.7 1512.0
## - gender:reading_score                    1    35.094 4132.5 1512.4
## + lunch_type:wkly_study_hours             2     5.815 4091.6 1512.6
## + gender:wkly_study_hours                 2     5.566 4091.8 1512.6
## - practice_sport:is_first_child           2    50.834 4148.2 1512.7
## - ethnic_group:math_score                 4    79.418 4176.8 1512.7
## + is_first_child:wkly_study_hours         2     2.132 4095.3 1513.1
## + gender:practice_sport                   2     0.708 4096.7 1513.3
## + gender:parent_marital_status            3    12.246 4085.2 1513.7
## + parent_marital_status:is_first_child    3     8.289 4089.1 1514.2
## + parent_educ:test_prep                   5    35.209 4062.2 1514.3
## + parent_marital_status:transport_means   3     7.493 4089.9 1514.3
## + parent_marital_status:reading_score     3     6.629 4090.8 1514.5
## + parent_marital_status:math_score        3     2.609 4094.8 1515.0
## - test_prep:parent_marital_status         3    83.334 4180.7 1515.3
## + parent_marital_status:practice_sport    5    27.648 4069.8 1515.4
## + practice_sport:wkly_study_hours         4    12.169 4085.2 1515.7
## + ethnic_group:reading_score              4    10.902 4086.5 1515.8
## - ethnic_group:wkly_study_hours           8   160.497 4257.9 1516.1
## + gender:parent_educ                      5    18.627 4078.8 1516.7
## - parent_educ:practice_sport             10   197.362 4294.8 1517.2
## - ethnic_group:lunch_type                 4   126.663 4224.1 1519.4
## + parent_educ:wkly_study_hours           10    61.565 4035.8 1520.5
## - math_score:reading_score                1    96.451 4193.9 1521.1
## + parent_educ:parent_marital_status      15   115.485 3981.9 1522.5
## - parent_educ:is_first_child              5   200.148 4297.6 1527.5
## 
## Step:  AIC=1506.2
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:parent_marital_status     11   134.418 4495.4 1502.1
## - ethnic_group:transport_means            4    32.236 4393.2 1502.5
## - practice_sport:transport_means          2     5.631 4366.6 1503.0
## - wkly_study_hours:math_score             2     6.347 4367.3 1503.0
## - test_prep:wkly_study_hours              2    11.717 4372.7 1503.8
## - gender:transport_means                  1     0.001 4361.0 1504.2
## - is_first_child:reading_score            1     0.511 4361.5 1504.3
## - is_first_child:transport_means          1     0.534 4361.5 1504.3
## - test_prep:reading_score                 1     0.572 4361.6 1504.3
## - lunch_type:test_prep                    1     0.970 4362.0 1504.3
## - gender:test_prep                        1     0.988 4362.0 1504.3
## - gender:is_first_child                   1     1.346 4362.3 1504.4
## - lunch_type:transport_means              1     1.360 4362.3 1504.4
## - transport_means:reading_score           1     1.361 4362.3 1504.4
## - gender:lunch_type                       1     1.677 4362.7 1504.4
## - test_prep:math_score                    1     1.705 4362.7 1504.4
## - lunch_type:practice_sport               2    17.004 4378.0 1504.5
## - lunch_type:is_first_child               1     2.606 4363.6 1504.5
## - ethnic_group:is_first_child             4    47.337 4408.3 1504.6
## - is_first_child:math_score               1     4.124 4365.1 1504.8
## - lunch_type:reading_score                1     5.589 4366.6 1505.0
## - wkly_study_hours:reading_score          2    21.181 4382.2 1505.0
## - transport_means:wkly_study_hours        2    22.891 4383.9 1505.3
## - lunch_type:parent_marital_status        3    38.402 4399.4 1505.4
## - ethnic_group:practice_sport             8   114.739 4475.7 1505.5
## - lunch_type:math_score                   1    10.093 4371.1 1505.6
## - transport_means:math_score              1    10.722 4371.7 1505.6
## <none>                                                4361.0 1506.2
## - test_prep:transport_means               1    15.367 4376.4 1506.3
## - parent_educ:transport_means             5    76.924 4437.9 1506.5
## - ethnic_group:test_prep                  4    62.614 4423.6 1506.6
## - gender:math_score                       1    20.385 4381.4 1507.0
## - ethnic_group:wkly_study_hours           8   128.477 4489.5 1507.3
## - test_prep:is_first_child                1    25.974 4387.0 1507.7
## - test_prep:practice_sport                2    42.685 4403.7 1507.9
## - parent_educ:lunch_type                  5    87.760 4448.7 1508.0
## - gender:reading_score                    1    36.592 4397.6 1509.1
## - test_prep:parent_marital_status         3    68.234 4429.2 1509.4
## + ethnic_group:parent_educ               20   263.576 4097.4 1509.4
## + gender:wkly_study_hours                 2     5.111 4355.9 1509.5
## + gender:practice_sport                   2     2.941 4358.0 1509.8
## - practice_sport:reading_score            2    56.869 4417.9 1509.8
## + parent_educ:test_prep                   5    45.848 4315.1 1510.0
## + is_first_child:wkly_study_hours         2     1.422 4359.6 1510.0
## + lunch_type:wkly_study_hours             2     1.063 4359.9 1510.0
## - practice_sport:math_score               2    61.393 4422.4 1510.4
## + gender:parent_marital_status            3    11.490 4349.5 1510.6
## + parent_marital_status:transport_means   3    10.758 4350.2 1510.7
## - gender:ethnic_group                     4    96.203 4457.2 1511.1
## + ethnic_group:reading_score              4    21.138 4339.9 1511.3
## - practice_sport:is_first_child           2    68.564 4429.6 1511.4
## - parent_educ:practice_sport             10   190.937 4551.9 1511.5
## + parent_marital_status:reading_score     3     4.661 4356.3 1511.6
## + parent_marital_status:is_first_child    3     3.138 4357.9 1511.8
## - parent_educ:reading_score               5   117.945 4478.9 1511.9
## + parent_marital_status:math_score        3     1.533 4359.5 1512.0
## - ethnic_group:math_score                 4   104.152 4465.1 1512.1
## - ethnic_group:lunch_type                 4   108.376 4469.4 1512.7
## + parent_marital_status:practice_sport    5    24.797 4336.2 1512.8
## + practice_sport:wkly_study_hours         4     9.527 4351.5 1512.9
## - parent_marital_status:wkly_study_hours  6   144.757 4505.7 1513.5
## + gender:parent_educ                      5    19.663 4341.3 1513.5
## - parent_educ:math_score                  5   138.040 4499.0 1514.6
## - math_score:reading_score                1    81.843 4442.8 1515.2
## + parent_educ:wkly_study_hours           10    58.684 4302.3 1518.2
## + parent_educ:parent_marital_status      15    92.872 4268.1 1523.5
## - parent_educ:is_first_child              5   223.461 4584.4 1525.7
## 
## Step:  AIC=1502.11
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - practice_sport:transport_means          2     6.574 4502.0 1499.0
## - ethnic_group:transport_means            4    38.691 4534.1 1499.2
## - wkly_study_hours:math_score             2     9.432 4504.8 1499.3
## - lunch_type:practice_sport               2    13.541 4508.9 1499.9
## - test_prep:wkly_study_hours              2    14.600 4510.0 1500.0
## - test_prep:reading_score                 1     0.012 4495.4 1500.1
## - gender:transport_means                  1     0.042 4495.4 1500.1
## - gender:test_prep                        1     0.126 4495.5 1500.1
## - is_first_child:reading_score            1     0.144 4495.6 1500.1
## - gender:is_first_child                   1     0.301 4495.7 1500.2
## - transport_means:reading_score           1     0.497 4495.9 1500.2
## - lunch_type:test_prep                    1     0.545 4496.0 1500.2
## - test_prep:math_score                    1     0.849 4496.3 1500.2
## - lunch_type:transport_means              1     1.070 4496.5 1500.2
## - is_first_child:transport_means          1     1.141 4496.5 1500.3
## - is_first_child:math_score               1     1.781 4497.2 1500.3
## - gender:lunch_type                       1     2.369 4497.8 1500.4
## - ethnic_group:practice_sport             8   112.148 4607.6 1500.6
## - lunch_type:is_first_child               1     4.532 4499.9 1500.7
## - transport_means:wkly_study_hours        2    21.660 4517.1 1500.9
## - lunch_type:reading_score                1     8.568 4504.0 1501.2
## - ethnic_group:wkly_study_hours           8   119.694 4615.1 1501.6
## - wkly_study_hours:reading_score          2    26.990 4522.4 1501.6
## - lunch_type:math_score                   1    12.057 4507.5 1501.7
## - transport_means:math_score              1    13.386 4508.8 1501.9
## <none>                                                4495.4 1502.1
## - gender:math_score                       1    18.673 4514.1 1502.5
## - ethnic_group:test_prep                  4    65.054 4560.5 1502.6
## - test_prep:transport_means               1    20.287 4515.7 1502.8
## - test_prep:practice_sport                2    36.294 4531.7 1502.8
## - test_prep:is_first_child                1    20.998 4516.4 1502.9
## - lunch_type:parent_marital_status        3    56.233 4551.6 1503.4
## - parent_educ:lunch_type                  5    89.811 4585.2 1503.8
## - gender:reading_score                    1    33.309 4528.7 1504.5
## - gender:ethnic_group                     4    82.724 4578.1 1504.9
## + parent_educ:test_prep                   5    54.502 4440.9 1504.9
## - practice_sport:reading_score            2    52.308 4547.7 1504.9
## - ethnic_group:lunch_type                 4    83.783 4579.2 1505.0
## - ethnic_group:is_first_child             4    83.832 4579.2 1505.0
## + gender:wkly_study_hours                 2     7.158 4488.2 1505.2
## - ethnic_group:math_score                 4    87.135 4582.5 1505.4
## + lunch_type:wkly_study_hours             2     4.681 4490.7 1505.5
## - test_prep:parent_marital_status         3    72.321 4567.7 1505.5
## + gender:practice_sport                   2     3.977 4491.4 1505.6
## + is_first_child:wkly_study_hours         2     3.785 4491.6 1505.6
## - practice_sport:math_score               2    58.279 4553.7 1505.7
## - parent_educ:reading_score               5   108.609 4604.0 1506.2
## + ethnic_group:parent_marital_status     11   134.418 4361.0 1506.2
## + parent_marital_status:math_score        3    12.758 4482.6 1506.4
## - parent_educ:transport_means             5   111.205 4606.6 1506.5
## + gender:parent_marital_status            3     9.390 4486.0 1506.9
## + parent_marital_status:is_first_child    3     8.174 4487.2 1507.0
## + parent_marital_status:transport_means   3     7.879 4487.5 1507.1
## + ethnic_group:reading_score              4    20.469 4474.9 1507.4
## + parent_marital_status:reading_score     3     4.279 4491.1 1507.5
## - practice_sport:is_first_child           2    74.367 4569.8 1507.8
## - parent_educ:practice_sport             10   201.040 4696.4 1507.9
## + gender:parent_educ                      5    31.588 4463.8 1508.0
## + practice_sport:wkly_study_hours         4    10.191 4485.2 1508.8
## + ethnic_group:parent_educ               20   240.994 4254.4 1509.6
## + parent_marital_status:practice_sport    5    17.201 4478.2 1509.8
## - math_score:reading_score                1    75.306 4570.7 1509.9
## - parent_marital_status:wkly_study_hours  6   154.607 4650.0 1510.1
## - parent_educ:math_score                  5   140.960 4636.4 1510.3
## + parent_educ:wkly_study_hours           10    55.302 4440.1 1514.8
## + parent_educ:parent_marital_status      15    96.005 4399.4 1519.4
## - parent_educ:is_first_child              5   232.016 4727.4 1521.8
## 
## Step:  AIC=1498.97
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:transport_means            4    39.294 4541.3 1496.1
## - wkly_study_hours:math_score             2     8.759 4510.7 1496.1
## - lunch_type:practice_sport               2    14.244 4516.2 1496.8
## - test_prep:wkly_study_hours              2    14.931 4516.9 1496.9
## - test_prep:reading_score                 1     0.014 4502.0 1497.0
## - gender:transport_means                  1     0.060 4502.0 1497.0
## - gender:test_prep                        1     0.094 4502.1 1497.0
## - is_first_child:reading_score            1     0.164 4502.1 1497.0
## - lunch_type:test_prep                    1     0.257 4502.2 1497.0
## - transport_means:reading_score           1     0.414 4502.4 1497.0
## - gender:is_first_child                   1     0.417 4502.4 1497.0
## - test_prep:math_score                    1     0.716 4502.7 1497.1
## - lunch_type:transport_means              1     1.196 4503.2 1497.1
## - is_first_child:transport_means          1     1.353 4503.3 1497.2
## - is_first_child:math_score               1     1.824 4503.8 1497.2
## - ethnic_group:practice_sport             8   110.626 4612.6 1497.3
## - gender:lunch_type                       1     2.609 4504.6 1497.3
## - lunch_type:is_first_child               1     4.894 4506.9 1497.6
## - transport_means:wkly_study_hours        2    21.177 4523.2 1497.7
## - lunch_type:reading_score                1     9.135 4511.1 1498.2
## - wkly_study_hours:reading_score          2    25.732 4527.7 1498.3
## - ethnic_group:wkly_study_hours           8   119.308 4621.3 1498.4
## - lunch_type:math_score                   1    13.188 4515.2 1498.7
## - transport_means:math_score              1    14.206 4516.2 1498.8
## <none>                                                4502.0 1499.0
## - ethnic_group:test_prep                  4    64.842 4566.8 1499.4
## - gender:math_score                       1    18.910 4520.9 1499.4
## - test_prep:transport_means               1    19.360 4521.3 1499.5
## - test_prep:practice_sport                2    36.247 4538.2 1499.7
## - test_prep:is_first_child                1    21.281 4523.3 1499.8
## - parent_educ:lunch_type                  5    85.799 4587.8 1500.1
## - lunch_type:parent_marital_status        3    56.389 4558.4 1500.3
## - gender:reading_score                    1    33.313 4535.3 1501.3
## - ethnic_group:lunch_type                 4    81.670 4583.7 1501.6
## - ethnic_group:is_first_child             4    81.850 4583.8 1501.6
## - gender:ethnic_group                     4    82.950 4584.9 1501.7
## - practice_sport:reading_score            2    52.533 4554.5 1501.8
## + gender:wkly_study_hours                 2     7.571 4494.4 1502.0
## + practice_sport:transport_means          2     6.574 4495.4 1502.1
## + parent_educ:test_prep                   5    51.220 4450.8 1502.2
## - ethnic_group:math_score                 4    87.116 4589.1 1502.3
## + lunch_type:wkly_study_hours             2     5.277 4496.7 1502.3
## - test_prep:parent_marital_status         3    72.176 4574.2 1502.3
## + is_first_child:wkly_study_hours         2     4.127 4497.9 1502.4
## - parent_educ:reading_score               5   105.055 4607.0 1502.6
## - practice_sport:math_score               2    58.496 4560.5 1502.6
## + gender:practice_sport                   2     1.476 4500.5 1502.8
## + ethnic_group:parent_marital_status     11   135.361 4366.6 1503.0
## + parent_marital_status:math_score        3    13.230 4488.7 1503.2
## - parent_educ:transport_means             5   110.982 4613.0 1503.3
## + gender:parent_marital_status            3    10.756 4491.2 1503.6
## + parent_marital_status:transport_means   3     8.613 4493.4 1503.8
## + parent_marital_status:is_first_child    3     8.082 4493.9 1503.9
## - practice_sport:is_first_child           2    68.870 4570.8 1503.9
## + ethnic_group:reading_score              4    20.497 4481.5 1504.3
## + parent_marital_status:reading_score     3     4.363 4497.6 1504.4
## + gender:parent_educ                      5    30.245 4471.7 1505.0
## + practice_sport:wkly_study_hours         4     9.874 4492.1 1505.7
## + ethnic_group:parent_educ               20   239.979 4262.0 1506.7
## - parent_educ:practice_sport             10   216.463 4718.4 1506.7
## - parent_educ:math_score                  5   137.228 4639.2 1506.7
## - parent_marital_status:wkly_study_hours  6   153.546 4655.5 1506.8
## - math_score:reading_score                1    77.678 4579.7 1507.1
## + parent_marital_status:practice_sport    5    14.426 4487.6 1507.1
## + parent_educ:wkly_study_hours           10    53.209 4448.8 1512.0
## + parent_educ:parent_marital_status      15    93.540 4408.4 1516.6
## - parent_educ:is_first_child              5   226.491 4728.5 1517.9
## 
## Step:  AIC=1496.1
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:practice_sport             8    96.429 4637.7 1492.5
## - wkly_study_hours:math_score             2     7.298 4548.6 1493.0
## - lunch_type:practice_sport               2    11.585 4552.9 1493.6
## - test_prep:reading_score                 1     0.013 4541.3 1494.1
## - gender:transport_means                  1     0.042 4541.3 1494.1
## - lunch_type:transport_means              1     0.102 4541.4 1494.1
## - test_prep:wkly_study_hours              2    15.638 4556.9 1494.1
## - is_first_child:transport_means          1     0.288 4541.6 1494.1
## - gender:test_prep                        1     0.312 4541.6 1494.1
## - is_first_child:reading_score            1     0.396 4541.7 1494.2
## - lunch_type:test_prep                    1     0.600 4541.9 1494.2
## - gender:is_first_child                   1     0.755 4542.0 1494.2
## - test_prep:math_score                    1     1.214 4542.5 1494.2
## - transport_means:reading_score           1     2.124 4543.4 1494.4
## - lunch_type:is_first_child               1     2.715 4544.0 1494.5
## - is_first_child:math_score               1     2.892 4544.2 1494.5
## - gender:lunch_type                       1     3.521 4544.8 1494.5
## - wkly_study_hours:reading_score          2    20.590 4561.9 1494.8
## - transport_means:wkly_study_hours        2    20.818 4562.1 1494.8
## - transport_means:math_score              1     6.279 4547.6 1494.9
## - ethnic_group:wkly_study_hours           8   116.236 4657.5 1495.0
## - lunch_type:reading_score                1     9.568 4550.8 1495.3
## - lunch_type:math_score                   1    14.031 4555.3 1495.9
## <none>                                                4541.3 1496.1
## - test_prep:transport_means               1    15.745 4557.0 1496.1
## - gender:math_score                       1    17.894 4559.2 1496.4
## - test_prep:is_first_child                1    18.069 4559.3 1496.4
## - lunch_type:parent_marital_status        3    53.969 4595.2 1497.1
## - parent_educ:lunch_type                  5    85.288 4626.6 1497.1
## - test_prep:practice_sport                2    38.672 4579.9 1497.1
## - ethnic_group:test_prep                  4    72.370 4613.6 1497.4
## - ethnic_group:lunch_type                 4    75.587 4616.9 1497.8
## - ethnic_group:math_score                 4    78.862 4620.1 1498.2
## - gender:reading_score                    1    33.037 4574.3 1498.4
## - gender:ethnic_group                     4    81.290 4622.6 1498.6
## - ethnic_group:is_first_child             4    83.265 4624.5 1498.8
## + ethnic_group:transport_means            4    39.294 4502.0 1499.0
## - practice_sport:is_first_child           2    53.275 4594.5 1499.0
## - practice_sport:math_score               2    53.899 4595.2 1499.1
## + lunch_type:wkly_study_hours             2     7.667 4533.6 1499.1
## + practice_sport:transport_means          2     7.177 4534.1 1499.2
## + gender:wkly_study_hours                 2     7.008 4534.3 1499.2
## - practice_sport:reading_score            2    55.144 4596.4 1499.2
## - parent_educ:reading_score               5   103.125 4644.4 1499.3
## + ethnic_group:parent_marital_status     11   141.691 4399.6 1499.4
## + is_first_child:wkly_study_hours         2     4.483 4536.8 1499.5
## - test_prep:parent_marital_status         3    73.182 4614.5 1499.5
## + gender:practice_sport                   2     1.645 4539.6 1499.9
## + parent_educ:test_prep                   5    47.414 4493.9 1499.9
## + parent_marital_status:math_score        3    13.231 4528.0 1500.4
## - parent_educ:transport_means             5   112.659 4653.9 1500.5
## + parent_marital_status:is_first_child    3    11.482 4529.8 1500.6
## + gender:parent_marital_status            3    11.307 4530.0 1500.6
## + ethnic_group:reading_score              4    25.545 4515.7 1500.8
## + parent_marital_status:transport_means   3    10.154 4531.1 1500.8
## + parent_marital_status:reading_score     3     4.706 4536.6 1501.5
## + gender:parent_educ                      5    31.575 4509.7 1502.0
## + practice_sport:wkly_study_hours         4    13.182 4528.1 1502.4
## - parent_marital_status:wkly_study_hours  6   152.759 4694.0 1503.6
## + parent_marital_status:practice_sport    5    17.602 4523.7 1503.8
## - parent_educ:math_score                  5   139.191 4680.5 1503.9
## - parent_educ:practice_sport             10   219.914 4761.2 1504.0
## - math_score:reading_score                1    81.156 4622.4 1504.5
## + ethnic_group:parent_educ               20   219.620 4321.7 1506.8
## + parent_educ:wkly_study_hours           10    50.863 4490.4 1509.5
## - parent_educ:is_first_child              5   212.675 4753.9 1513.1
## + parent_educ:parent_marital_status      15    94.199 4447.1 1513.7
## 
## Step:  AIC=1492.49
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:math_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:practice_sport               2     4.085 4641.8 1489.0
## - wkly_study_hours:math_score             2     6.449 4644.2 1489.3
## - lunch_type:transport_means              1     0.074 4637.8 1490.5
## - test_prep:reading_score                 1     0.139 4637.8 1490.5
## - gender:test_prep                        1     0.151 4637.9 1490.5
## - is_first_child:reading_score            1     0.249 4638.0 1490.5
## - gender:transport_means                  1     0.278 4638.0 1490.5
## - is_first_child:transport_means          1     0.298 4638.0 1490.5
## - gender:is_first_child                   1     0.505 4638.2 1490.6
## - test_prep:math_score                    1     1.442 4639.1 1490.7
## - lunch_type:test_prep                    1     1.951 4639.7 1490.7
## - is_first_child:math_score               1     2.153 4639.9 1490.8
## - transport_means:reading_score           1     2.187 4639.9 1490.8
## - lunch_type:is_first_child               1     2.476 4640.2 1490.8
## - wkly_study_hours:reading_score          2    19.258 4657.0 1490.9
## - gender:lunch_type                       1     3.719 4641.4 1491.0
## - transport_means:math_score              1     4.069 4641.8 1491.0
## - ethnic_group:wkly_study_hours           8   115.791 4753.5 1491.0
## - lunch_type:reading_score                1     8.648 4646.4 1491.6
## - test_prep:wkly_study_hours              2    24.732 4662.4 1491.6
## - transport_means:wkly_study_hours        2    24.919 4662.6 1491.7
## - lunch_type:math_score                   1    10.028 4647.7 1491.8
## - test_prep:transport_means               1    14.354 4652.1 1492.3
## - gender:math_score                       1    15.348 4653.1 1492.4
## <none>                                                4637.7 1492.5
## - test_prep:is_first_child                1    16.028 4653.7 1492.5
## - practice_sport:math_score               2    36.073 4673.8 1493.1
## - ethnic_group:lunch_type                 4    69.121 4706.8 1493.2
## - test_prep:practice_sport                2    38.874 4676.6 1493.4
## - practice_sport:is_first_child           2    39.068 4676.8 1493.4
## - ethnic_group:test_prep                  4    72.397 4710.1 1493.6
## - lunch_type:parent_marital_status        3    59.365 4697.1 1494.0
## - test_prep:parent_marital_status         3    61.317 4699.0 1494.2
## - practice_sport:reading_score            2    46.317 4684.0 1494.4
## - parent_educ:reading_score               5    95.049 4732.8 1494.5
## + parent_educ:test_prep                   5    62.211 4575.5 1494.5
## - parent_educ:lunch_type                  5    95.606 4733.3 1494.5
## - ethnic_group:is_first_child             4    80.750 4718.5 1494.7
## - ethnic_group:math_score                 4    81.516 4719.2 1494.8
## - gender:reading_score                    1    35.259 4673.0 1495.0
## - parent_educ:transport_means             5    99.690 4737.4 1495.0
## + lunch_type:wkly_study_hours             2    10.433 4627.3 1495.2
## - gender:ethnic_group                     4    86.497 4724.2 1495.4
## + gender:wkly_study_hours                 2     6.782 4630.9 1495.6
## + practice_sport:transport_means          2     4.487 4633.2 1495.9
## + is_first_child:wkly_study_hours         2     4.122 4633.6 1496.0
## + ethnic_group:practice_sport             8    96.429 4541.3 1496.1
## + gender:practice_sport                   2     0.947 4636.8 1496.4
## + parent_marital_status:is_first_child    3    15.429 4622.3 1496.5
## + gender:parent_marital_status            3    14.004 4623.7 1496.7
## + ethnic_group:parent_marital_status     11   137.275 4500.4 1496.8
## + parent_marital_status:math_score        3     9.548 4628.2 1497.3
## + ethnic_group:transport_means            4    25.098 4612.6 1497.3
## + gender:parent_educ                      5    39.651 4598.1 1497.4
## + parent_marital_status:reading_score     3     4.793 4632.9 1497.9
## + parent_marital_status:transport_means   3     4.767 4632.9 1497.9
## + ethnic_group:reading_score              4    19.236 4618.5 1498.0
## + practice_sport:wkly_study_hours         4    16.993 4620.7 1498.3
## - parent_educ:math_score                  5   126.716 4764.4 1498.4
## - math_score:reading_score                1    72.425 4710.1 1499.6
## - parent_marital_status:wkly_study_hours  6   155.932 4793.6 1500.0
## + parent_marital_status:practice_sport    5     9.052 4628.7 1501.3
## + ethnic_group:parent_educ               20   230.479 4407.2 1502.4
## - parent_educ:practice_sport             10   241.622 4879.3 1502.5
## + parent_educ:wkly_study_hours           10    50.368 4587.3 1506.0
## - parent_educ:is_first_child              5   204.434 4842.1 1507.9
## + parent_educ:parent_marital_status      15    86.973 4550.7 1511.3
## 
## Step:  AIC=1489.01
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:math_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - wkly_study_hours:math_score             2     6.427 4648.2 1485.8
## - gender:test_prep                        1     0.123 4641.9 1487.0
## - test_prep:reading_score                 1     0.140 4641.9 1487.0
## - lunch_type:transport_means              1     0.149 4641.9 1487.0
## - is_first_child:reading_score            1     0.231 4642.0 1487.0
## - gender:transport_means                  1     0.288 4642.1 1487.0
## - is_first_child:transport_means          1     0.312 4642.1 1487.0
## - gender:is_first_child                   1     0.860 4642.6 1487.1
## - test_prep:math_score                    1     1.461 4643.2 1487.2
## - is_first_child:math_score               1     2.168 4644.0 1487.3
## - transport_means:reading_score           1     2.209 4644.0 1487.3
## - lunch_type:test_prep                    1     2.407 4644.2 1487.3
## - lunch_type:is_first_child               1     2.689 4644.5 1487.3
## - wkly_study_hours:reading_score          2    19.621 4661.4 1487.5
## - gender:lunch_type                       1     4.059 4645.8 1487.5
## - transport_means:math_score              1     4.252 4646.0 1487.5
## - ethnic_group:wkly_study_hours           8   119.442 4761.2 1488.0
## - transport_means:wkly_study_hours        2    24.620 4666.4 1488.1
## - lunch_type:reading_score                1     8.850 4650.6 1488.1
## - test_prep:wkly_study_hours              2    24.865 4666.7 1488.2
## - lunch_type:math_score                   1    10.454 4652.2 1488.3
## - test_prep:transport_means               1    14.600 4656.4 1488.9
## - gender:math_score                       1    15.269 4657.1 1489.0
## <none>                                                4641.8 1489.0
## - test_prep:is_first_child                1    16.166 4658.0 1489.1
## - practice_sport:math_score               2    36.464 4678.3 1489.6
## - ethnic_group:lunch_type                 4    68.330 4710.1 1489.6
## - practice_sport:is_first_child           2    38.300 4680.1 1489.9
## - test_prep:practice_sport                2    40.658 4682.4 1490.2
## - lunch_type:parent_marital_status        3    57.927 4699.7 1490.3
## - ethnic_group:test_prep                  4    75.611 4717.4 1490.5
## - test_prep:parent_marital_status         3    61.908 4703.7 1490.8
## - practice_sport:reading_score            2    46.395 4688.2 1490.9
## + parent_educ:test_prep                   5    61.804 4580.0 1491.1
## - parent_educ:lunch_type                  5    97.292 4739.1 1491.2
## - ethnic_group:math_score                 4    81.582 4723.4 1491.3
## - ethnic_group:is_first_child             4    82.123 4723.9 1491.4
## - gender:reading_score                    1    34.973 4676.8 1491.4
## - parent_educ:reading_score               5    98.886 4740.7 1491.5
## - parent_educ:transport_means             5    99.299 4741.1 1491.5
## + lunch_type:wkly_study_hours             2    11.648 4630.1 1491.5
## - gender:ethnic_group                     4    85.470 4727.3 1491.8
## + gender:wkly_study_hours                 2     6.493 4635.3 1492.2
## + practice_sport:transport_means          2     4.564 4637.2 1492.4
## + lunch_type:practice_sport               2     4.085 4637.7 1492.5
## + is_first_child:wkly_study_hours         2     3.504 4638.3 1492.6
## + gender:practice_sport                   2     0.821 4641.0 1492.9
## + parent_marital_status:is_first_child    3    15.435 4626.4 1493.0
## + gender:parent_marital_status            3    11.727 4630.1 1493.5
## + ethnic_group:practice_sport             8    88.930 4552.9 1493.6
## + parent_marital_status:math_score        3     9.220 4632.6 1493.8
## + ethnic_group:transport_means            4    24.602 4617.2 1493.9
## + ethnic_group:parent_marital_status     11   132.686 4509.1 1493.9
## + gender:parent_educ                      5    40.019 4601.8 1493.9
## + parent_marital_status:transport_means   3     5.189 4636.6 1494.3
## + parent_marital_status:reading_score     3     4.223 4637.6 1494.5
## + practice_sport:wkly_study_hours         4    18.074 4623.7 1494.7
## + ethnic_group:reading_score              4    17.890 4623.9 1494.7
## - parent_educ:math_score                  5   132.009 4773.8 1495.6
## - math_score:reading_score                1    74.022 4715.8 1496.3
## - parent_marital_status:wkly_study_hours  6   156.704 4798.5 1496.6
## + parent_marital_status:practice_sport    5     8.623 4633.2 1497.9
## - parent_educ:practice_sport             10   240.847 4882.6 1498.9
## + ethnic_group:parent_educ               20   230.953 4410.8 1498.9
## + parent_educ:wkly_study_hours           10    50.143 4591.6 1502.6
## - parent_educ:is_first_child              5   204.050 4845.8 1504.4
## + parent_educ:parent_marital_status      15    86.947 4554.8 1507.9
## 
## Step:  AIC=1485.83
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:transport_means              1     0.026 4648.2 1483.8
## - gender:test_prep                        1     0.071 4648.3 1483.8
## - is_first_child:transport_means          1     0.110 4648.3 1483.8
## - test_prep:reading_score                 1     0.220 4648.4 1483.9
## - is_first_child:reading_score            1     0.227 4648.4 1483.9
## - gender:transport_means                  1     0.389 4648.6 1483.9
## - gender:is_first_child                   1     0.786 4649.0 1483.9
## - test_prep:math_score                    1     1.079 4649.3 1484.0
## - lunch_type:test_prep                    1     2.009 4650.2 1484.1
## - is_first_child:math_score               1     2.350 4650.6 1484.1
## - lunch_type:is_first_child               1     2.799 4651.0 1484.2
## - transport_means:reading_score           1     2.907 4651.1 1484.2
## - wkly_study_hours:reading_score          2    19.694 4667.9 1484.3
## - transport_means:math_score              1     3.933 4652.1 1484.3
## - gender:lunch_type                       1     4.189 4652.4 1484.4
## - ethnic_group:wkly_study_hours           8   119.047 4767.3 1484.8
## - lunch_type:reading_score                1     8.695 4656.9 1484.9
## - test_prep:wkly_study_hours              2    25.007 4673.2 1485.0
## - transport_means:wkly_study_hours        2    25.270 4673.5 1485.0
## - lunch_type:math_score                   1    10.472 4658.7 1485.2
## - test_prep:is_first_child                1    14.916 4663.1 1485.7
## - test_prep:transport_means               1    14.951 4663.2 1485.7
## <none>                                                4648.2 1485.8
## - gender:math_score                       1    15.820 4664.0 1485.8
## - ethnic_group:lunch_type                 4    67.085 4715.3 1486.3
## - practice_sport:is_first_child           2    37.888 4686.1 1486.6
## - practice_sport:math_score               2    37.997 4686.2 1486.6
## - test_prep:practice_sport                2    40.293 4688.5 1486.9
## - lunch_type:parent_marital_status        3    56.961 4705.2 1487.0
## - ethnic_group:test_prep                  4    77.070 4725.3 1487.5
## - ethnic_group:is_first_child             4    78.587 4726.8 1487.7
## - test_prep:parent_marital_status         3    62.700 4710.9 1487.7
## - practice_sport:reading_score            2    47.095 4695.3 1487.8
## - parent_educ:reading_score               5    95.264 4743.5 1487.8
## + parent_educ:test_prep                   5    62.680 4585.5 1487.8
## - ethnic_group:math_score                 4    80.544 4728.8 1488.0
## - parent_educ:lunch_type                  5    97.718 4745.9 1488.1
## - gender:reading_score                    1    35.271 4683.5 1488.3
## - gender:ethnic_group                     4    83.861 4732.1 1488.4
## - parent_educ:transport_means             5   101.826 4750.0 1488.6
## + lunch_type:wkly_study_hours             2     7.442 4640.8 1488.9
## + gender:wkly_study_hours                 2     6.525 4641.7 1489.0
## + wkly_study_hours:math_score             2     6.427 4641.8 1489.0
## + lunch_type:practice_sport               2     4.062 4644.2 1489.3
## + practice_sport:transport_means          2     4.015 4644.2 1489.3
## + is_first_child:wkly_study_hours         2     3.694 4644.5 1489.4
## + parent_marital_status:is_first_child    3    16.635 4631.6 1489.7
## + gender:practice_sport                   2     0.686 4647.5 1489.7
## + gender:parent_marital_status            3    10.989 4637.2 1490.4
## + ethnic_group:parent_marital_status     11   134.787 4513.4 1490.5
## + ethnic_group:practice_sport             8    88.305 4559.9 1490.5
## + parent_marital_status:math_score        3     9.142 4639.1 1490.7
## + gender:parent_educ                      5    39.318 4608.9 1490.8
## + ethnic_group:transport_means            4    23.168 4625.0 1490.9
## + parent_marital_status:transport_means   3     4.747 4643.5 1491.2
## + parent_marital_status:reading_score     3     3.854 4644.4 1491.3
## + practice_sport:wkly_study_hours         4    18.055 4630.2 1491.5
## + ethnic_group:reading_score              4    16.389 4631.8 1491.7
## - parent_educ:math_score                  5   127.156 4775.4 1491.8
## - parent_marital_status:wkly_study_hours  6   155.995 4804.2 1493.3
## - math_score:reading_score                1    79.762 4728.0 1493.9
## + parent_marital_status:practice_sport    5     7.945 4640.3 1494.8
## - parent_educ:practice_sport             10   238.468 4886.7 1495.3
## + ethnic_group:parent_educ               20   230.919 4417.3 1495.8
## + parent_educ:wkly_study_hours           10    50.066 4598.1 1499.4
## - parent_educ:is_first_child              5   206.513 4854.7 1501.5
## + parent_educ:parent_marital_status      15    86.486 4561.7 1504.8
## 
## Step:  AIC=1483.83
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:is_first_child + gender:transport_means + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:test_prep                        1     0.074 4648.3 1481.8
## - is_first_child:transport_means          1     0.107 4648.3 1481.8
## - test_prep:reading_score                 1     0.213 4648.5 1481.9
## - is_first_child:reading_score            1     0.221 4648.5 1481.9
## - gender:transport_means                  1     0.371 4648.6 1481.9
## - gender:is_first_child                   1     0.770 4649.0 1481.9
## - test_prep:math_score                    1     1.087 4649.3 1482.0
## - lunch_type:test_prep                    1     1.983 4650.2 1482.1
## - is_first_child:math_score               1     2.331 4650.6 1482.1
## - lunch_type:is_first_child               1     2.822 4651.1 1482.2
## - transport_means:reading_score           1     2.894 4651.1 1482.2
## - wkly_study_hours:reading_score          2    19.712 4668.0 1482.3
## - gender:lunch_type                       1     4.164 4652.4 1482.4
## - transport_means:math_score              1     4.562 4652.8 1482.4
## - ethnic_group:wkly_study_hours           8   119.025 4767.3 1482.8
## - lunch_type:reading_score                1     8.684 4656.9 1482.9
## - test_prep:wkly_study_hours              2    25.028 4673.3 1483.0
## - transport_means:wkly_study_hours        2    25.263 4673.5 1483.0
## - lunch_type:math_score                   1    10.448 4658.7 1483.2
## - test_prep:is_first_child                1    14.891 4663.1 1483.7
## - test_prep:transport_means               1    15.219 4663.5 1483.8
## <none>                                                4648.2 1483.8
## - gender:math_score                       1    15.824 4664.1 1483.8
## - ethnic_group:lunch_type                 4    67.082 4715.3 1484.3
## - practice_sport:math_score               2    37.978 4686.2 1484.6
## - practice_sport:is_first_child           2    38.149 4686.4 1484.7
## - test_prep:practice_sport                2    40.583 4688.8 1485.0
## - lunch_type:parent_marital_status        3    57.060 4705.3 1485.0
## - ethnic_group:test_prep                  4    77.046 4725.3 1485.5
## - ethnic_group:is_first_child             4    78.561 4726.8 1485.7
## - test_prep:parent_marital_status         3    62.818 4711.1 1485.8
## - practice_sport:reading_score            2    47.096 4695.3 1485.8
## - parent_educ:reading_score               5    95.258 4743.5 1485.8
## + lunch_type:transport_means              1     0.026 4648.2 1485.8
## + parent_educ:test_prep                   5    62.521 4585.7 1485.8
## - ethnic_group:math_score                 4    81.338 4729.6 1486.1
## - parent_educ:lunch_type                  5    98.765 4747.0 1486.2
## - gender:reading_score                    1    35.292 4683.5 1486.3
## - gender:ethnic_group                     4    83.902 4732.1 1486.4
## - parent_educ:transport_means             5   102.584 4750.8 1486.7
## + lunch_type:wkly_study_hours             2     7.468 4640.8 1486.9
## + gender:wkly_study_hours                 2     6.486 4641.8 1487.0
## + wkly_study_hours:math_score             2     6.304 4641.9 1487.0
## + lunch_type:practice_sport               2     4.085 4644.2 1487.3
## + practice_sport:transport_means          2     4.015 4644.2 1487.3
## + is_first_child:wkly_study_hours         2     3.683 4644.6 1487.4
## + parent_marital_status:is_first_child    3    16.654 4631.6 1487.7
## + gender:practice_sport                   2     0.680 4647.6 1487.8
## + gender:parent_marital_status            3    11.007 4637.2 1488.4
## + ethnic_group:parent_marital_status     11   134.597 4513.6 1488.5
## + ethnic_group:practice_sport             8    88.262 4560.0 1488.5
## + parent_marital_status:math_score        3     9.127 4639.1 1488.7
## + gender:parent_educ                      5    39.289 4609.0 1488.8
## + ethnic_group:transport_means            4    23.187 4625.1 1488.9
## + parent_marital_status:transport_means   3     4.693 4643.5 1489.2
## + parent_marital_status:reading_score     3     3.852 4644.4 1489.3
## + practice_sport:wkly_study_hours         4    18.008 4630.2 1489.5
## + ethnic_group:reading_score              4    16.391 4631.9 1489.8
## - parent_educ:math_score                  5   127.542 4775.8 1489.8
## - parent_marital_status:wkly_study_hours  6   156.016 4804.3 1491.3
## - math_score:reading_score                1    79.775 4728.0 1491.9
## + parent_marital_status:practice_sport    5     7.971 4640.3 1492.8
## - parent_educ:practice_sport             10   239.279 4887.5 1493.5
## + ethnic_group:parent_educ               20   230.416 4417.8 1493.8
## + parent_educ:wkly_study_hours           10    50.091 4598.2 1497.4
## - parent_educ:is_first_child              5   207.196 4855.4 1499.6
## + parent_educ:parent_marital_status      15    86.332 4561.9 1502.8
## 
## Step:  AIC=1481.84
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:is_first_child + 
##     gender:transport_means + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:math_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - is_first_child:transport_means          1     0.105 4648.4 1479.8
## - is_first_child:reading_score            1     0.248 4648.6 1479.9
## - gender:transport_means                  1     0.334 4648.6 1479.9
## - gender:is_first_child                   1     0.816 4649.1 1479.9
## - test_prep:reading_score                 1     0.888 4649.2 1480.0
## - test_prep:math_score                    1     1.367 4649.7 1480.0
## - lunch_type:test_prep                    1     1.924 4650.2 1480.1
## - is_first_child:math_score               1     2.427 4650.7 1480.2
## - lunch_type:is_first_child               1     2.821 4651.1 1480.2
## - transport_means:reading_score           1     2.843 4651.2 1480.2
## - wkly_study_hours:reading_score          2    19.679 4668.0 1480.3
## - gender:lunch_type                       1     4.303 4652.6 1480.4
## - transport_means:math_score              1     4.724 4653.0 1480.4
## - ethnic_group:wkly_study_hours           8   118.980 4767.3 1480.8
## - lunch_type:reading_score                1     8.703 4657.0 1480.9
## - test_prep:wkly_study_hours              2    25.175 4673.5 1481.0
## - transport_means:wkly_study_hours        2    25.220 4673.5 1481.0
## - lunch_type:math_score                   1    10.455 4658.8 1481.2
## - test_prep:is_first_child                1    14.822 4663.1 1481.7
## - test_prep:transport_means               1    15.259 4663.6 1481.8
## <none>                                                4648.3 1481.8
## - gender:math_score                       1    15.842 4664.2 1481.8
## - ethnic_group:lunch_type                 4    67.486 4715.8 1482.3
## - practice_sport:math_score               2    37.911 4686.2 1482.6
## - practice_sport:is_first_child           2    38.084 4686.4 1482.7
## - test_prep:practice_sport                2    40.531 4688.8 1483.0
## - lunch_type:parent_marital_status        3    57.389 4705.7 1483.1
## - ethnic_group:test_prep                  4    78.008 4726.3 1483.7
## - ethnic_group:is_first_child             4    78.672 4727.0 1483.7
## - test_prep:parent_marital_status         3    62.798 4711.1 1483.8
## - practice_sport:reading_score            2    47.031 4695.3 1483.8
## - parent_educ:reading_score               5    95.200 4743.5 1483.8
## + gender:test_prep                        1     0.074 4648.2 1483.8
## + lunch_type:transport_means              1     0.029 4648.3 1483.8
## + parent_educ:test_prep                   5    62.588 4585.7 1483.8
## - parent_educ:lunch_type                  5    98.913 4747.2 1484.3
## - gender:ethnic_group                     4    83.877 4732.2 1484.4
## - ethnic_group:math_score                 4    83.975 4732.3 1484.4
## - gender:reading_score                    1    36.167 4684.5 1484.4
## - parent_educ:transport_means             5   102.675 4751.0 1484.7
## + lunch_type:wkly_study_hours             2     7.492 4640.8 1484.9
## + gender:wkly_study_hours                 2     6.490 4641.8 1485.0
## + wkly_study_hours:math_score             2     6.246 4642.1 1485.0
## + lunch_type:practice_sport               2     4.061 4644.3 1485.3
## + practice_sport:transport_means          2     3.983 4644.3 1485.3
## + is_first_child:wkly_study_hours         2     3.636 4644.7 1485.4
## + parent_marital_status:is_first_child    3    16.723 4631.6 1485.7
## + gender:practice_sport                   2     0.699 4647.6 1485.8
## + gender:parent_marital_status            3    11.013 4637.3 1486.4
## + ethnic_group:practice_sport             8    88.113 4560.2 1486.5
## + ethnic_group:parent_marital_status     11   134.041 4514.3 1486.6
## + parent_marital_status:math_score        3     8.879 4639.4 1486.7
## + gender:parent_educ                      5    39.291 4609.0 1486.8
## + ethnic_group:transport_means            4    23.252 4625.1 1486.9
## + parent_marital_status:transport_means   3     4.720 4643.6 1487.2
## + parent_marital_status:reading_score     3     3.755 4644.6 1487.4
## + practice_sport:wkly_study_hours         4    18.033 4630.3 1487.5
## + ethnic_group:reading_score              4    16.374 4631.9 1487.8
## - parent_educ:math_score                  5   127.698 4776.0 1487.8
## - parent_marital_status:wkly_study_hours  6   156.389 4804.7 1489.4
## - math_score:reading_score                1    79.768 4728.1 1489.9
## + parent_marital_status:practice_sport    5     7.992 4640.3 1490.8
## - parent_educ:practice_sport             10   239.270 4887.6 1491.5
## + ethnic_group:parent_educ               20   230.488 4417.8 1491.8
## + parent_educ:wkly_study_hours           10    50.163 4598.2 1495.4
## - parent_educ:is_first_child              5   207.139 4855.5 1497.6
## + parent_educ:parent_marital_status      15    86.357 4562.0 1500.8
## 
## Step:  AIC=1479.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:is_first_child + 
##     gender:transport_means + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:math_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - is_first_child:reading_score            1     0.239 4648.7 1477.9
## - gender:transport_means                  1     0.341 4648.8 1477.9
## - gender:is_first_child                   1     0.808 4649.2 1478.0
## - test_prep:reading_score                 1     0.896 4649.3 1478.0
## - test_prep:math_score                    1     1.374 4649.8 1478.0
## - lunch_type:test_prep                    1     1.885 4650.3 1478.1
## - is_first_child:math_score               1     2.375 4650.8 1478.2
## - transport_means:reading_score           1     2.818 4651.2 1478.2
## - lunch_type:is_first_child               1     2.829 4651.2 1478.2
## - wkly_study_hours:reading_score          2    19.628 4668.0 1478.3
## - gender:lunch_type                       1     4.406 4652.8 1478.4
## - transport_means:math_score              1     4.780 4653.2 1478.5
## - ethnic_group:wkly_study_hours           8   119.009 4767.4 1478.8
## - lunch_type:reading_score                1     8.777 4657.2 1479.0
## - test_prep:wkly_study_hours              2    25.107 4673.5 1479.0
## - transport_means:wkly_study_hours        2    25.213 4673.6 1479.0
## - lunch_type:math_score                   1    10.512 4658.9 1479.2
## - test_prep:is_first_child                1    14.729 4663.1 1479.7
## - test_prep:transport_means               1    15.162 4663.6 1479.8
## - gender:math_score                       1    15.772 4664.2 1479.8
## <none>                                                4648.4 1479.8
## - ethnic_group:lunch_type                 4    67.786 4716.2 1480.4
## - practice_sport:math_score               2    37.870 4686.3 1480.6
## - practice_sport:is_first_child           2    37.984 4686.4 1480.7
## - test_prep:practice_sport                2    40.488 4688.9 1481.0
## - lunch_type:parent_marital_status        3    57.457 4705.9 1481.1
## - ethnic_group:test_prep                  4    77.905 4726.3 1481.7
## - test_prep:parent_marital_status         3    62.761 4711.2 1481.8
## - ethnic_group:is_first_child             4    78.859 4727.3 1481.8
## - practice_sport:reading_score            2    46.927 4695.3 1481.8
## - parent_educ:reading_score               5    95.095 4743.5 1481.8
## + is_first_child:transport_means          1     0.105 4648.3 1481.8
## + gender:test_prep                        1     0.072 4648.3 1481.8
## + lunch_type:transport_means              1     0.025 4648.4 1481.8
## + parent_educ:test_prep                   5    62.413 4586.0 1481.9
## - parent_educ:lunch_type                  5    99.214 4747.6 1482.3
## - gender:reading_score                    1    36.071 4684.5 1482.4
## - gender:ethnic_group                     4    84.147 4732.6 1482.4
## - ethnic_group:math_score                 4    84.614 4733.0 1482.5
## - parent_educ:transport_means             5   103.296 4751.7 1482.8
## + lunch_type:wkly_study_hours             2     7.370 4641.1 1482.9
## + gender:wkly_study_hours                 2     6.427 4642.0 1483.0
## + wkly_study_hours:math_score             2     6.061 4642.4 1483.1
## + lunch_type:practice_sport               2     4.064 4644.4 1483.3
## + practice_sport:transport_means          2     3.922 4644.5 1483.4
## + is_first_child:wkly_study_hours         2     3.537 4644.9 1483.4
## + parent_marital_status:is_first_child    3    16.731 4631.7 1483.7
## + gender:practice_sport                   2     0.682 4647.7 1483.8
## + gender:parent_marital_status            3    11.118 4637.3 1484.4
## + ethnic_group:parent_marital_status     11   133.866 4514.6 1484.6
## + ethnic_group:practice_sport             8    87.692 4560.7 1484.6
## + parent_marital_status:math_score        3     8.943 4639.5 1484.7
## + gender:parent_educ                      5    39.248 4609.2 1484.8
## + ethnic_group:transport_means            4    23.356 4625.1 1484.9
## + parent_marital_status:transport_means   3     4.498 4643.9 1485.3
## + parent_marital_status:reading_score     3     3.834 4644.6 1485.4
## + practice_sport:wkly_study_hours         4    18.038 4630.4 1485.6
## + ethnic_group:reading_score              4    16.349 4632.1 1485.8
## - parent_educ:math_score                  5   127.726 4776.1 1485.8
## - parent_marital_status:wkly_study_hours  6   156.336 4804.8 1487.4
## - math_score:reading_score                1    79.679 4728.1 1487.9
## + parent_marital_status:practice_sport    5     7.860 4640.6 1488.9
## - parent_educ:practice_sport             10   239.206 4887.6 1489.5
## + ethnic_group:parent_educ               20   230.555 4417.9 1489.8
## + parent_educ:wkly_study_hours           10    50.250 4598.2 1493.4
## - parent_educ:is_first_child              5   207.039 4855.5 1495.6
## + parent_educ:parent_marital_status      15    86.450 4562.0 1498.8
## 
## Step:  AIC=1477.88
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:is_first_child + 
##     gender:transport_means + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:wkly_study_hours + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:transport_means                  1     0.291 4648.9 1475.9
## - gender:is_first_child                   1     0.616 4649.3 1476.0
## - test_prep:reading_score                 1     0.788 4649.4 1476.0
## - test_prep:math_score                    1     1.516 4650.2 1476.1
## - lunch_type:test_prep                    1     1.836 4650.5 1476.1
## - transport_means:reading_score           1     2.671 4651.3 1476.2
## - lunch_type:is_first_child               1     2.960 4651.6 1476.3
## - wkly_study_hours:reading_score          2    19.472 4668.1 1476.3
## - gender:lunch_type                       1     4.430 4653.1 1476.5
## - transport_means:math_score              1     4.981 4653.6 1476.5
## - is_first_child:math_score               1     6.092 4654.8 1476.7
## - ethnic_group:wkly_study_hours           8   118.881 4767.5 1476.8
## - lunch_type:reading_score                1     8.914 4657.6 1477.0
## - transport_means:wkly_study_hours        2    25.394 4674.1 1477.1
## - test_prep:wkly_study_hours              2    25.414 4674.1 1477.1
## - lunch_type:math_score                   1    10.575 4659.2 1477.2
## - test_prep:transport_means               1    15.087 4663.7 1477.8
## <none>                                                4648.7 1477.9
## - gender:math_score                       1    15.835 4664.5 1477.9
## - test_prep:is_first_child                1    15.907 4664.6 1477.9
## - ethnic_group:lunch_type                 4    68.561 4717.2 1478.5
## - practice_sport:math_score               2    38.140 4686.8 1478.7
## - practice_sport:is_first_child           2    39.353 4688.0 1478.9
## - test_prep:practice_sport                2    40.528 4689.2 1479.0
## - lunch_type:parent_marital_status        3    57.349 4706.0 1479.1
## - ethnic_group:test_prep                  4    77.673 4726.3 1479.7
## - test_prep:parent_marital_status         3    62.564 4711.2 1479.8
## - ethnic_group:is_first_child             4    78.625 4727.3 1479.8
## - parent_educ:reading_score               5    94.865 4743.5 1479.8
## - practice_sport:reading_score            2    47.016 4695.7 1479.8
## + is_first_child:reading_score            1     0.239 4648.4 1479.8
## + gender:test_prep                        1     0.098 4648.6 1479.9
## + is_first_child:transport_means          1     0.096 4648.6 1479.9
## + lunch_type:transport_means              1     0.019 4648.6 1479.9
## + parent_educ:test_prep                   5    62.585 4586.1 1479.9
## - parent_educ:lunch_type                  5    99.061 4747.7 1480.3
## - gender:ethnic_group                     4    83.910 4732.6 1480.4
## - gender:reading_score                    1    36.548 4685.2 1480.5
## - ethnic_group:math_score                 4    85.778 4734.4 1480.7
## + lunch_type:wkly_study_hours             2     7.309 4641.4 1481.0
## - parent_educ:transport_means             5   104.343 4753.0 1481.0
## + gender:wkly_study_hours                 2     6.312 4642.3 1481.1
## + wkly_study_hours:math_score             2     6.065 4642.6 1481.1
## + lunch_type:practice_sport               2     4.039 4644.6 1481.4
## + practice_sport:transport_means          2     3.925 4644.7 1481.4
## + is_first_child:wkly_study_hours         2     3.341 4645.3 1481.5
## + gender:practice_sport                   2     0.644 4648.0 1481.8
## + parent_marital_status:is_first_child    3    16.285 4632.4 1481.8
## + gender:parent_marital_status            3    11.032 4637.6 1482.5
## + ethnic_group:practice_sport             8    87.421 4561.2 1482.7
## + ethnic_group:parent_marital_status     11   133.249 4515.4 1482.7
## + parent_marital_status:math_score        3     8.830 4639.8 1482.8
## + gender:parent_educ                      5    39.486 4609.2 1482.8
## + ethnic_group:transport_means            4    23.478 4625.2 1482.9
## + parent_marital_status:transport_means   3     4.449 4644.2 1483.3
## + parent_marital_status:reading_score     3     3.832 4644.8 1483.4
## + practice_sport:wkly_study_hours         4    18.024 4630.6 1483.6
## + ethnic_group:reading_score              4    16.267 4632.4 1483.8
## - parent_educ:math_score                  5   127.558 4776.2 1483.9
## - parent_marital_status:wkly_study_hours  6   156.239 4804.9 1485.4
## - math_score:reading_score                1    79.440 4728.1 1485.9
## + parent_marital_status:practice_sport    5     7.766 4640.9 1486.9
## - parent_educ:practice_sport             10   239.245 4887.9 1487.5
## + ethnic_group:parent_educ               20   230.659 4418.0 1487.9
## + parent_educ:wkly_study_hours           10    50.240 4598.4 1491.5
## - parent_educ:is_first_child              5   207.310 4856.0 1493.6
## + parent_educ:parent_marital_status      15    86.311 4562.3 1496.8
## 
## Step:  AIC=1475.92
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:is_first_child + 
##     gender:math_score + gender:reading_score + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:is_first_child                   1     0.646 4649.6 1474.0
## - test_prep:reading_score                 1     0.807 4649.8 1474.0
## - test_prep:math_score                    1     1.476 4650.4 1474.1
## - lunch_type:test_prep                    1     1.879 4650.8 1474.2
## - lunch_type:is_first_child               1     2.904 4651.9 1474.3
## - transport_means:reading_score           1     2.960 4651.9 1474.3
## - wkly_study_hours:reading_score          2    19.352 4668.3 1474.4
## - gender:lunch_type                       1     4.450 4653.4 1474.5
## - is_first_child:math_score               1     6.378 4655.3 1474.7
## - ethnic_group:wkly_study_hours           8   118.989 4767.9 1474.8
## - lunch_type:reading_score                1     9.043 4658.0 1475.1
## - test_prep:wkly_study_hours              2    25.201 4674.2 1475.1
## - transport_means:wkly_study_hours        2    25.505 4674.5 1475.2
## - lunch_type:math_score                   1    10.853 4659.8 1475.3
## - transport_means:math_score              1    12.281 4661.2 1475.5
## - test_prep:transport_means               1    14.801 4663.8 1475.8
## <none>                                                4648.9 1475.9
## - test_prep:is_first_child                1    15.910 4664.9 1475.9
## - gender:math_score                       1    15.936 4664.9 1475.9
## - ethnic_group:lunch_type                 4    68.891 4717.8 1476.6
## - practice_sport:math_score               2    38.086 4687.0 1476.7
## - practice_sport:is_first_child           2    39.239 4688.2 1476.9
## - test_prep:practice_sport                2    40.712 4689.7 1477.1
## - lunch_type:parent_marital_status        3    57.363 4706.3 1477.2
## - ethnic_group:test_prep                  4    77.461 4726.4 1477.7
## - ethnic_group:is_first_child             4    78.382 4727.3 1477.8
## - test_prep:parent_marital_status         3    62.498 4711.4 1477.8
## - practice_sport:reading_score            2    47.129 4696.1 1477.9
## + gender:transport_means                  1     0.291 4648.7 1477.9
## + is_first_child:reading_score            1     0.189 4648.8 1477.9
## + is_first_child:transport_means          1     0.103 4648.8 1477.9
## + gender:test_prep                        1     0.055 4648.9 1477.9
## + lunch_type:transport_means              1     0.005 4648.9 1477.9
## + parent_educ:test_prep                   5    62.168 4586.8 1478.0
## - parent_educ:reading_score               5    96.004 4745.0 1478.0
## - parent_educ:lunch_type                  5   100.222 4749.2 1478.5
## - gender:ethnic_group                     4    84.208 4733.2 1478.5
## - gender:reading_score                    1    36.455 4685.4 1478.5
## - ethnic_group:math_score                 4    85.739 4734.7 1478.7
## + lunch_type:wkly_study_hours             2     7.280 4641.7 1479.0
## - parent_educ:transport_means             5   104.521 4753.5 1479.0
## + gender:wkly_study_hours                 2     6.387 4642.6 1479.1
## + wkly_study_hours:math_score             2     6.181 4642.8 1479.1
## + lunch_type:practice_sport               2     4.039 4644.9 1479.4
## + practice_sport:transport_means          2     3.942 4645.0 1479.4
## + is_first_child:wkly_study_hours         2     3.360 4645.6 1479.5
## + parent_marital_status:is_first_child    3    16.452 4632.5 1479.8
## + gender:practice_sport                   2     0.676 4648.3 1479.8
## + gender:parent_marital_status            3    10.918 4638.0 1480.5
## + ethnic_group:practice_sport             8    87.642 4561.3 1480.7
## + ethnic_group:parent_marital_status     11   133.271 4515.7 1480.8
## + parent_marital_status:math_score        3     8.776 4640.2 1480.8
## + gender:parent_educ                      5    39.681 4609.3 1480.9
## + ethnic_group:transport_means            4    23.429 4625.5 1480.9
## + parent_marital_status:transport_means   3     4.357 4644.6 1481.4
## + parent_marital_status:reading_score     3     3.820 4645.1 1481.4
## + practice_sport:wkly_study_hours         4    17.824 4631.1 1481.7
## + ethnic_group:reading_score              4    16.110 4632.8 1481.9
## - parent_educ:math_score                  5   128.216 4777.2 1482.0
## - parent_marital_status:wkly_study_hours  6   156.162 4805.1 1483.4
## - math_score:reading_score                1    79.598 4728.5 1483.9
## + parent_marital_status:practice_sport    5     7.580 4641.4 1485.0
## - parent_educ:practice_sport             10   239.461 4888.4 1485.5
## + ethnic_group:parent_educ               20   230.829 4418.1 1485.9
## + parent_educ:wkly_study_hours           10    50.235 4598.7 1489.5
## - parent_educ:is_first_child              5   207.115 4856.1 1491.6
## + parent_educ:parent_marital_status      15    86.331 4562.6 1494.9
## 
## Step:  AIC=1474
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     wkly_study_hours:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:reading_score                 1     0.973 4650.6 1472.1
## - test_prep:math_score                    1     1.342 4650.9 1472.2
## - lunch_type:test_prep                    1     1.709 4651.3 1472.2
## - transport_means:reading_score           1     2.844 4652.4 1472.4
## - lunch_type:is_first_child               1     3.027 4652.6 1472.4
## - wkly_study_hours:reading_score          2    19.293 4668.9 1472.5
## - gender:lunch_type                       1     4.223 4653.8 1472.5
## - is_first_child:math_score               1     5.825 4655.4 1472.7
## - ethnic_group:wkly_study_hours           8   118.653 4768.2 1472.9
## - lunch_type:reading_score                1     8.657 4658.3 1473.1
## - test_prep:wkly_study_hours              2    25.266 4674.9 1473.2
## - transport_means:wkly_study_hours        2    25.356 4675.0 1473.2
## - lunch_type:math_score                   1    10.484 4660.1 1473.3
## - transport_means:math_score              1    12.091 4661.7 1473.5
## - test_prep:transport_means               1    14.727 4664.3 1473.9
## <none>                                                4649.6 1474.0
## - gender:math_score                       1    16.218 4665.8 1474.1
## - test_prep:is_first_child                1    16.668 4666.3 1474.1
## - ethnic_group:lunch_type                 4    68.692 4718.3 1474.7
## - practice_sport:math_score               2    37.950 4687.5 1474.8
## - practice_sport:is_first_child           2    38.724 4688.3 1474.9
## - test_prep:practice_sport                2    40.252 4689.8 1475.1
## - lunch_type:parent_marital_status        3    56.994 4706.6 1475.2
## - ethnic_group:test_prep                  4    76.913 4726.5 1475.7
## - ethnic_group:is_first_child             4    77.737 4727.3 1475.8
## - test_prep:parent_marital_status         3    62.182 4711.8 1475.8
## - practice_sport:reading_score            2    46.689 4696.3 1475.9
## + gender:is_first_child                   1     0.646 4648.9 1475.9
## + gender:transport_means                  1     0.321 4649.3 1476.0
## + is_first_child:transport_means          1     0.108 4649.5 1476.0
## + is_first_child:reading_score            1     0.071 4649.5 1476.0
## + gender:test_prep                        1     0.062 4649.5 1476.0
## + lunch_type:transport_means              1     0.001 4649.6 1476.0
## - parent_educ:reading_score               5    95.632 4745.2 1476.0
## + parent_educ:test_prep                   5    62.135 4587.5 1476.1
## - gender:ethnic_group                     4    83.567 4733.2 1476.5
## - parent_educ:lunch_type                  5   100.511 4750.1 1476.6
## - gender:reading_score                    1    37.103 4686.7 1476.7
## - ethnic_group:math_score                 4    85.598 4735.2 1476.8
## + lunch_type:wkly_study_hours             2     7.206 4642.4 1477.1
## + gender:wkly_study_hours                 2     6.314 4643.3 1477.2
## + wkly_study_hours:math_score             2     6.115 4643.5 1477.2
## - parent_educ:transport_means             5   105.414 4755.0 1477.2
## + lunch_type:practice_sport               2     4.449 4645.1 1477.4
## + practice_sport:transport_means          2     4.128 4645.5 1477.5
## + is_first_child:wkly_study_hours         2     3.022 4646.6 1477.6
## + parent_marital_status:is_first_child    3    16.767 4632.8 1477.9
## + gender:practice_sport                   2     0.568 4649.0 1477.9
## + gender:parent_marital_status            3    10.664 4638.9 1478.7
## + ethnic_group:practice_sport             8    87.418 4562.2 1478.8
## + parent_marital_status:math_score        3     8.633 4641.0 1478.9
## + gender:parent_educ                      5    39.096 4610.5 1479.0
## + ethnic_group:transport_means            4    23.351 4626.2 1479.0
## + ethnic_group:parent_marital_status     11   131.230 4518.4 1479.1
## + parent_marital_status:transport_means   3     4.615 4645.0 1479.4
## + parent_marital_status:reading_score     3     3.718 4645.9 1479.5
## + practice_sport:wkly_study_hours         4    17.860 4631.7 1479.7
## + ethnic_group:reading_score              4    16.424 4633.2 1479.9
## - parent_educ:math_score                  5   128.151 4777.7 1480.0
## - parent_marital_status:wkly_study_hours  6   155.564 4805.2 1481.4
## - math_score:reading_score                1    80.084 4729.7 1482.1
## + parent_marital_status:practice_sport    5     7.476 4642.1 1483.0
## - parent_educ:practice_sport             10   239.926 4889.5 1483.7
## + ethnic_group:parent_educ               20   228.660 4420.9 1484.2
## + parent_educ:wkly_study_hours           10    49.429 4600.2 1487.7
## - parent_educ:is_first_child              5   206.473 4856.1 1489.6
## + parent_educ:parent_marital_status      15    86.330 4563.3 1493.0
## 
## Step:  AIC=1472.13
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:test_prep                    1     2.058 4652.6 1470.4
## - lunch_type:is_first_child               1     3.240 4653.8 1470.5
## - wkly_study_hours:reading_score          2    19.153 4669.7 1470.5
## - transport_means:reading_score           1     3.354 4653.9 1470.5
## - gender:lunch_type                       1     4.125 4654.7 1470.7
## - is_first_child:math_score               1     6.076 4656.6 1470.9
## - ethnic_group:wkly_study_hours           8   119.207 4769.8 1471.1
## - test_prep:math_score                    1     8.298 4658.9 1471.2
## - lunch_type:reading_score                1     8.325 4658.9 1471.2
## - transport_means:wkly_study_hours        2    24.609 4675.2 1471.2
## - test_prep:wkly_study_hours              2    25.606 4676.2 1471.4
## - lunch_type:math_score                   1    10.301 4660.9 1471.4
## - transport_means:math_score              1    11.644 4662.2 1471.6
## - test_prep:transport_means               1    15.143 4665.7 1472.0
## <none>                                                4650.6 1472.1
## - test_prep:is_first_child                1    16.716 4667.3 1472.2
## - gender:math_score                       1    16.980 4667.5 1472.3
## - ethnic_group:lunch_type                 4    67.973 4718.5 1472.7
## - practice_sport:math_score               2    38.500 4689.1 1473.0
## - practice_sport:is_first_child           2    38.679 4689.2 1473.0
## - test_prep:practice_sport                2    41.371 4691.9 1473.3
## - lunch_type:parent_marital_status        3    58.052 4708.6 1473.5
## - ethnic_group:test_prep                  4    76.260 4726.8 1473.7
## - test_prep:parent_marital_status         3    61.566 4712.1 1473.9
## - ethnic_group:is_first_child             4    78.359 4728.9 1474.0
## + test_prep:reading_score                 1     0.973 4649.6 1474.0
## + gender:is_first_child                   1     0.812 4649.8 1474.0
## + gender:test_prep                        1     0.770 4649.8 1474.0
## + parent_educ:test_prep                   5    63.038 4587.5 1474.1
## + gender:transport_means                  1     0.347 4650.2 1474.1
## + is_first_child:reading_score            1     0.186 4650.4 1474.1
## + is_first_child:transport_means          1     0.120 4650.4 1474.1
## - practice_sport:reading_score            2    47.440 4698.0 1474.1
## + lunch_type:transport_means              1     0.000 4650.6 1474.1
## - parent_educ:reading_score               5    95.802 4746.4 1474.2
## - gender:ethnic_group                     4    82.715 4733.3 1474.5
## - ethnic_group:math_score                 4    85.462 4736.0 1474.9
## - parent_educ:lunch_type                  5   102.644 4753.2 1475.0
## - gender:reading_score                    1    38.805 4689.4 1475.0
## + lunch_type:wkly_study_hours             2     7.499 4643.1 1475.2
## + wkly_study_hours:math_score             2     6.215 4644.4 1475.3
## + gender:wkly_study_hours                 2     6.004 4644.6 1475.4
## - parent_educ:transport_means             5   106.330 4756.9 1475.5
## + lunch_type:practice_sport               2     4.449 4646.1 1475.6
## + practice_sport:transport_means          2     4.078 4646.5 1475.6
## + is_first_child:wkly_study_hours         2     3.049 4647.5 1475.7
## + parent_marital_status:is_first_child    3    17.169 4633.4 1475.9
## + gender:practice_sport                   2     0.522 4650.0 1476.1
## + gender:parent_marital_status            3    10.880 4639.7 1476.8
## + ethnic_group:practice_sport             8    88.117 4562.5 1476.8
## + parent_marital_status:math_score        3     8.755 4641.8 1477.0
## + gender:parent_educ                      5    39.051 4611.5 1477.2
## + ethnic_group:parent_marital_status     11   131.877 4518.7 1477.2
## + ethnic_group:transport_means            4    23.290 4627.3 1477.2
## + parent_marital_status:transport_means   3     4.664 4645.9 1477.5
## + parent_marital_status:reading_score     3     3.790 4646.8 1477.7
## + practice_sport:wkly_study_hours         4    17.801 4632.8 1477.9
## + ethnic_group:reading_score              4    16.558 4634.0 1478.0
## - parent_educ:math_score                  5   129.498 4780.1 1478.3
## - parent_marital_status:wkly_study_hours  6   157.100 4807.7 1479.7
## - math_score:reading_score                1    81.119 4731.7 1480.3
## + parent_marital_status:practice_sport    5     7.530 4643.0 1481.2
## - parent_educ:practice_sport             10   239.745 4890.3 1481.8
## + ethnic_group:parent_educ               20   228.646 4421.9 1482.4
## + parent_educ:wkly_study_hours           10    48.983 4601.6 1485.9
## - parent_educ:is_first_child              5   208.569 4859.1 1488.0
## + parent_educ:parent_marital_status      15    85.247 4565.3 1491.2
## 
## Step:  AIC=1470.39
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + wkly_study_hours:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - wkly_study_hours:reading_score          2    18.717 4671.3 1468.8
## - lunch_type:is_first_child               1     3.006 4655.6 1468.8
## - transport_means:reading_score           1     3.532 4656.2 1468.8
## - gender:lunch_type                       1     3.703 4656.3 1468.9
## - ethnic_group:wkly_study_hours           8   117.155 4769.8 1469.1
## - is_first_child:math_score               1     5.962 4658.6 1469.1
## - test_prep:math_score                    1     6.303 4658.9 1469.2
## - lunch_type:reading_score                1     7.384 4660.0 1469.3
## - test_prep:wkly_study_hours              2    24.822 4677.4 1469.5
## - transport_means:wkly_study_hours        2    25.450 4678.1 1469.6
## - lunch_type:math_score                   1    10.247 4662.9 1469.7
## - transport_means:math_score              1    11.271 4663.9 1469.8
## - test_prep:transport_means               1    15.609 4668.2 1470.4
## <none>                                                4652.6 1470.4
## - test_prep:is_first_child                1    16.899 4669.5 1470.5
## - gender:math_score                       1    17.132 4669.8 1470.6
## - ethnic_group:lunch_type                 4    67.657 4720.3 1470.9
## - practice_sport:is_first_child           2    37.719 4690.3 1471.2
## - practice_sport:math_score               2    38.098 4690.7 1471.2
## - lunch_type:parent_marital_status        3    56.250 4708.9 1471.5
## - test_prep:practice_sport                2    40.697 4693.3 1471.5
## - ethnic_group:test_prep                  4    75.720 4728.3 1471.9
## - test_prep:parent_marital_status         3    60.499 4713.1 1472.0
## - ethnic_group:is_first_child             4    77.019 4729.6 1472.1
## + lunch_type:test_prep                    1     2.058 4650.6 1472.1
## + test_prep:reading_score                 1     1.323 4651.3 1472.2
## + parent_educ:test_prep                   5    63.592 4589.0 1472.3
## + gender:test_prep                        1     0.776 4651.9 1472.3
## + gender:is_first_child                   1     0.630 4652.0 1472.3
## - practice_sport:reading_score            2    47.020 4699.6 1472.3
## + gender:transport_means                  1     0.397 4652.2 1472.3
## + is_first_child:reading_score            1     0.173 4652.5 1472.4
## - parent_educ:reading_score               5    95.465 4748.1 1472.4
## + is_first_child:transport_means          1     0.080 4652.5 1472.4
## + lunch_type:transport_means              1     0.036 4652.6 1472.4
## - gender:ethnic_group                     4    82.358 4735.0 1472.7
## - parent_educ:lunch_type                  5   100.671 4753.3 1473.0
## - ethnic_group:math_score                 4    85.072 4737.7 1473.1
## - gender:reading_score                    1    38.860 4691.5 1473.3
## + lunch_type:wkly_study_hours             2     8.197 4644.4 1473.3
## - parent_educ:transport_means             5   105.075 4757.7 1473.6
## + wkly_study_hours:math_score             2     5.997 4646.6 1473.6
## + gender:wkly_study_hours                 2     5.745 4646.9 1473.7
## + lunch_type:practice_sport               2     4.805 4647.8 1473.8
## + practice_sport:transport_means          2     3.484 4649.1 1474.0
## + is_first_child:wkly_study_hours         2     3.361 4649.3 1474.0
## + parent_marital_status:is_first_child    3    17.183 4635.4 1474.2
## + gender:practice_sport                   2     0.326 4652.3 1474.3
## + ethnic_group:practice_sport             8    89.413 4563.2 1474.9
## + gender:parent_marital_status            3    10.590 4642.0 1475.0
## + parent_marital_status:math_score        3     9.163 4643.5 1475.2
## + ethnic_group:transport_means            4    23.982 4628.6 1475.3
## + ethnic_group:parent_marital_status     11   132.395 4520.2 1475.4
## + gender:parent_educ                      5    38.868 4613.8 1475.4
## + parent_marital_status:transport_means   3     4.658 4648.0 1475.8
## + parent_marital_status:reading_score     3     3.783 4648.8 1475.9
## + practice_sport:wkly_study_hours         4    17.986 4634.6 1476.1
## + ethnic_group:reading_score              4    16.713 4635.9 1476.3
## - parent_educ:math_score                  5   129.320 4781.9 1476.6
## - parent_marital_status:wkly_study_hours  6   156.063 4808.7 1477.8
## - math_score:reading_score                1    87.153 4739.8 1479.3
## + parent_marital_status:practice_sport    5     7.708 4644.9 1479.4
## - parent_educ:practice_sport             10   239.948 4892.6 1480.1
## + ethnic_group:parent_educ               20   228.813 4423.8 1480.6
## + parent_educ:wkly_study_hours           10    49.974 4602.7 1484.0
## - parent_educ:is_first_child              5   206.810 4859.4 1486.0
## + parent_educ:parent_marital_status      15    85.389 4567.2 1489.5
## 
## Step:  AIC=1468.76
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:wkly_study_hours + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:wkly_study_hours           8   110.675 4782.0 1466.6
## - gender:lunch_type                       1     3.092 4674.4 1467.2
## - lunch_type:is_first_child               1     3.564 4674.9 1467.2
## - transport_means:reading_score           1     3.971 4675.3 1467.3
## - transport_means:wkly_study_hours        2    21.001 4692.3 1467.4
## - is_first_child:math_score               1     5.419 4676.8 1467.4
## - lunch_type:reading_score                1     5.991 4677.3 1467.5
## - test_prep:wkly_study_hours              2    22.692 4694.0 1467.6
## - test_prep:math_score                    1     6.986 4678.3 1467.6
## - lunch_type:math_score                   1     8.903 4680.2 1467.9
## - transport_means:math_score              1     9.271 4680.6 1467.9
## - ethnic_group:lunch_type                 4    60.942 4732.3 1468.4
## - test_prep:is_first_child                1    14.759 4686.1 1468.6
## <none>                                                4671.3 1468.8
## - gender:math_score                       1    17.474 4688.8 1469.0
## - practice_sport:is_first_child           2    35.441 4706.8 1469.2
## - test_prep:transport_means               1    19.860 4691.2 1469.3
## - practice_sport:math_score               2    38.079 4709.4 1469.5
## - test_prep:practice_sport                2    38.936 4710.3 1469.7
## - ethnic_group:test_prep                  4    71.096 4742.4 1469.7
## - test_prep:parent_marital_status         3    56.201 4727.5 1469.8
## - lunch_type:parent_marital_status        3    57.876 4729.2 1470.0
## - ethnic_group:is_first_child             4    74.560 4745.9 1470.1
## + parent_educ:test_prep                   5    67.127 4604.2 1470.2
## + wkly_study_hours:reading_score          2    18.717 4652.6 1470.4
## + lunch_type:test_prep                    1     1.623 4669.7 1470.5
## + test_prep:reading_score                 1     1.127 4670.2 1470.6
## + gender:test_prep                        1     0.612 4670.7 1470.7
## + gender:is_first_child                   1     0.578 4670.8 1470.7
## + is_first_child:reading_score            1     0.257 4671.1 1470.7
## + gender:transport_means                  1     0.249 4671.1 1470.7
## + lunch_type:transport_means              1     0.244 4671.1 1470.7
## + is_first_child:transport_means          1     0.039 4671.3 1470.8
## - practice_sport:reading_score            2    49.337 4720.7 1471.0
## - parent_educ:reading_score               5    97.784 4769.1 1471.0
## - parent_educ:lunch_type                  5    99.831 4771.2 1471.2
## - gender:ethnic_group                     4    84.193 4755.5 1471.3
## + lunch_type:wkly_study_hours             2    11.270 4660.1 1471.3
## + gender:wkly_study_hours                 2     9.260 4662.1 1471.6
## - gender:reading_score                    1    39.085 4710.4 1471.7
## + wkly_study_hours:math_score             2     6.049 4665.3 1472.0
## - parent_educ:transport_means             5   106.345 4777.7 1472.0
## + lunch_type:practice_sport               2     5.368 4666.0 1472.1
## - ethnic_group:math_score                 4    92.617 4764.0 1472.3
## + is_first_child:wkly_study_hours         2     2.954 4668.4 1472.4
## + parent_marital_status:is_first_child    3    18.631 4652.7 1472.4
## + practice_sport:transport_means          2     2.781 4668.6 1472.4
## + gender:practice_sport                   2     0.692 4670.7 1472.7
## + gender:parent_marital_status            3    12.675 4658.7 1473.2
## + ethnic_group:practice_sport             8    90.916 4580.4 1473.2
## + ethnic_group:parent_marital_status     11   135.175 4536.2 1473.4
## + parent_marital_status:math_score        3    10.154 4661.2 1473.5
## + gender:parent_educ                      5    39.098 4632.2 1473.8
## + parent_marital_status:transport_means   3     6.176 4665.2 1474.0
## + parent_marital_status:reading_score     3     4.863 4666.5 1474.1
## + ethnic_group:transport_means            4    19.875 4651.5 1474.2
## + ethnic_group:reading_score              4    18.726 4652.6 1474.4
## + practice_sport:wkly_study_hours         4    16.985 4654.4 1474.6
## - parent_educ:math_score                  5   127.829 4799.2 1474.7
## - math_score:reading_score                1    78.623 4750.0 1476.6
## - parent_marital_status:wkly_study_hours  6   166.681 4838.0 1477.4
## + parent_marital_status:practice_sport    5     8.333 4663.0 1477.7
## + ethnic_group:parent_educ               20   231.018 4440.3 1478.8
## - parent_educ:practice_sport             10   250.043 4921.4 1479.5
## + parent_educ:wkly_study_hours           10    49.669 4621.7 1482.5
## - parent_educ:is_first_child              5   208.635 4880.0 1484.5
## + parent_educ:parent_marital_status      15    84.066 4587.3 1488.0
## 
## Step:  AIC=1466.57
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:math_score + parent_educ:lunch_type + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:math_score + 
##     transport_means:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - is_first_child:math_score               1     1.182 4783.2 1464.7
## - gender:lunch_type                       1     1.928 4783.9 1464.8
## - lunch_type:reading_score                1     4.088 4786.1 1465.1
## - transport_means:wkly_study_hours        2    20.969 4803.0 1465.2
## - transport_means:reading_score           1     5.140 4787.2 1465.2
## - lunch_type:math_score                   1     5.171 4787.2 1465.2
## - transport_means:math_score              1     5.903 4787.9 1465.3
## - lunch_type:is_first_child               1     7.970 4790.0 1465.5
## - test_prep:math_score                    1     8.701 4790.7 1465.6
## - test_prep:is_first_child                1    12.308 4794.3 1466.1
## - test_prep:wkly_study_hours              2    29.311 4811.3 1466.2
## - test_prep:parent_marital_status         3    46.188 4828.2 1466.2
## - test_prep:transport_means               1    16.016 4798.0 1466.5
## <none>                                                4782.0 1466.6
## - ethnic_group:lunch_type                 4    65.689 4847.7 1466.6
## - practice_sport:math_score               2    34.438 4816.5 1466.8
## - gender:math_score                       1    19.755 4801.8 1467.0
## - ethnic_group:is_first_child             4    69.381 4851.4 1467.1
## - lunch_type:parent_marital_status        3    54.647 4836.7 1467.3
## - test_prep:practice_sport                2    39.005 4821.0 1467.4
## - practice_sport:is_first_child           2    40.026 4822.0 1467.5
## - practice_sport:reading_score            2    42.005 4824.0 1467.7
## - parent_educ:reading_score               5    93.930 4875.9 1468.0
## + parent_educ:test_prep                   5    68.036 4714.0 1468.1
## - gender:ethnic_group                     4    79.023 4861.0 1468.2
## + test_prep:reading_score                 1     1.285 4780.7 1468.4
## + is_first_child:reading_score            1     1.024 4781.0 1468.5
## + gender:is_first_child                   1     0.492 4781.5 1468.5
## + gender:test_prep                        1     0.419 4781.6 1468.5
## + gender:transport_means                  1     0.362 4781.7 1468.5
## + is_first_child:transport_means          1     0.155 4781.9 1468.5
## + lunch_type:transport_means              1     0.096 4781.9 1468.6
## + lunch_type:test_prep                    1     0.008 4782.0 1468.6
## + ethnic_group:wkly_study_hours           8   110.675 4671.3 1468.8
## + wkly_study_hours:reading_score          2    12.237 4769.8 1469.1
## - parent_educ:lunch_type                  5   103.689 4885.7 1469.2
## + lunch_type:wkly_study_hours             2    10.874 4771.1 1469.2
## - ethnic_group:math_score                 4    89.968 4872.0 1469.6
## + lunch_type:practice_sport               2     7.998 4774.0 1469.6
## - gender:reading_score                    1    40.909 4822.9 1469.6
## + gender:wkly_study_hours                 2     6.097 4775.9 1469.8
## - ethnic_group:test_prep                  4    92.510 4874.5 1469.9
## + practice_sport:transport_means          2     3.723 4778.3 1470.1
## + wkly_study_hours:math_score             2     2.164 4779.9 1470.3
## + is_first_child:wkly_study_hours         2     1.462 4780.6 1470.4
## + gender:parent_marital_status            3    17.134 4764.9 1470.5
## + gender:practice_sport                   2     0.532 4781.5 1470.5
## + parent_marital_status:is_first_child    3    14.764 4767.3 1470.8
## + parent_marital_status:math_score        3    10.602 4771.4 1471.3
## - parent_educ:transport_means             5   120.741 4902.8 1471.3
## - parent_educ:math_score                  5   121.030 4903.0 1471.3
## + parent_marital_status:transport_means   3     9.757 4772.3 1471.4
## + ethnic_group:reading_score              4    25.436 4756.6 1471.4
## + parent_marital_status:reading_score     3     5.725 4776.3 1471.9
## + ethnic_group:practice_sport             8    85.057 4697.0 1472.0
## + gender:parent_educ                      5    35.964 4746.1 1472.1
## + ethnic_group:transport_means            4    17.989 4764.0 1472.3
## + ethnic_group:parent_marital_status     11   125.547 4656.5 1472.9
## + practice_sport:wkly_study_hours         4     6.691 4775.3 1473.8
## - parent_marital_status:wkly_study_hours  6   164.411 4946.4 1474.5
## - math_score:reading_score                1    84.761 4866.8 1474.9
## + parent_marital_status:practice_sport    5     4.190 4777.8 1476.1
## - parent_educ:practice_sport             10   260.322 5042.3 1477.8
## + ethnic_group:parent_educ               20   213.449 4568.6 1479.6
## - parent_educ:is_first_child              5   196.318 4978.3 1480.3
## + parent_educ:wkly_study_hours           10    35.027 4747.0 1482.2
## + parent_educ:parent_marital_status      15    95.972 4686.0 1484.6
## 
## Step:  AIC=1464.72
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:math_score + 
##     gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:math_score + parent_educ:lunch_type + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:lunch_type                       1     1.941 4785.1 1463.0
## - lunch_type:reading_score                1     3.941 4787.1 1463.2
## - transport_means:reading_score           1     4.872 4788.1 1463.3
## - lunch_type:math_score                   1     5.207 4788.4 1463.4
## - transport_means:wkly_study_hours        2    21.524 4804.7 1463.4
## - transport_means:math_score              1     5.990 4789.2 1463.5
## - test_prep:math_score                    1     8.301 4791.5 1463.7
## - test_prep:is_first_child                1    11.399 4794.6 1464.1
## - lunch_type:is_first_child               1    12.411 4795.6 1464.2
## - test_prep:wkly_study_hours              2    29.413 4812.6 1464.3
## - test_prep:parent_marital_status         3    45.849 4829.1 1464.3
## - test_prep:transport_means               1    15.876 4799.1 1464.7
## <none>                                                4783.2 1464.7
## - ethnic_group:lunch_type                 4    65.597 4848.8 1464.8
## - practice_sport:math_score               2    34.075 4817.3 1464.9
## - gender:math_score                       1    19.288 4802.5 1465.1
## - ethnic_group:is_first_child             4    68.617 4851.8 1465.1
## - lunch_type:parent_marital_status        3    54.323 4837.5 1465.4
## - test_prep:practice_sport                2    39.983 4823.2 1465.6
## - practice_sport:is_first_child           2    40.111 4823.3 1465.7
## - practice_sport:reading_score            2    41.819 4825.0 1465.8
## - parent_educ:reading_score               5    92.914 4876.1 1466.1
## + parent_educ:test_prep                   5    68.072 4715.1 1466.3
## - gender:ethnic_group                     4    78.569 4861.8 1466.3
## + is_first_child:reading_score            1     2.187 4781.0 1466.5
## + test_prep:reading_score                 1     1.395 4781.8 1466.5
## + is_first_child:math_score               1     1.182 4782.0 1466.6
## + gender:test_prep                        1     0.483 4782.7 1466.7
## + gender:transport_means                  1     0.467 4782.7 1466.7
## + gender:is_first_child                   1     0.227 4783.0 1466.7
## + lunch_type:transport_means              1     0.116 4783.1 1466.7
## + is_first_child:transport_means          1     0.094 4783.1 1466.7
## + lunch_type:test_prep                    1     0.008 4783.2 1466.7
## + wkly_study_hours:reading_score          2    12.031 4771.2 1467.2
## - parent_educ:lunch_type                  5   102.967 4886.2 1467.3
## + lunch_type:wkly_study_hours             2    10.546 4772.7 1467.4
## + ethnic_group:wkly_study_hours           8   106.437 4676.8 1467.4
## - gender:reading_score                    1    40.293 4823.5 1467.7
## + lunch_type:practice_sport               2     8.053 4775.1 1467.7
## - ethnic_group:math_score                 4    90.566 4873.8 1467.8
## + gender:wkly_study_hours                 2     6.321 4776.9 1467.9
## - ethnic_group:test_prep                  4    93.047 4876.2 1468.1
## + practice_sport:transport_means          2     3.724 4779.5 1468.3
## + wkly_study_hours:math_score             2     2.008 4781.2 1468.5
## + is_first_child:wkly_study_hours         2     1.288 4781.9 1468.6
## + gender:parent_marital_status            3    17.165 4766.0 1468.6
## + gender:practice_sport                   2     0.548 4782.7 1468.7
## + parent_marital_status:is_first_child    3    14.759 4768.4 1468.9
## - parent_educ:math_score                  5   120.430 4903.6 1469.4
## - parent_educ:transport_means             5   120.842 4904.0 1469.4
## + parent_marital_status:math_score        3    10.264 4772.9 1469.5
## + parent_marital_status:transport_means   3     9.795 4773.4 1469.5
## + ethnic_group:reading_score              4    25.829 4757.4 1469.5
## + parent_marital_status:reading_score     3     5.389 4777.8 1470.0
## + ethnic_group:practice_sport             8    84.129 4699.1 1470.2
## + gender:parent_educ                      5    36.031 4747.2 1470.3
## + ethnic_group:transport_means            4    18.379 4764.8 1470.5
## + ethnic_group:parent_marital_status     11   124.113 4659.1 1471.2
## + practice_sport:wkly_study_hours         4     7.001 4776.2 1471.8
## - parent_marital_status:wkly_study_hours  6   166.770 4950.0 1472.9
## - math_score:reading_score                1    91.806 4875.0 1473.9
## + parent_marital_status:practice_sport    5     4.360 4778.8 1474.2
## - parent_educ:practice_sport             10   260.127 5043.3 1476.0
## + ethnic_group:parent_educ               20   213.547 4569.7 1477.8
## - parent_educ:is_first_child              5   201.760 4985.0 1479.1
## + parent_educ:wkly_study_hours           10    35.100 4748.1 1480.4
## + parent_educ:parent_marital_status      15    95.698 4687.5 1482.8
## 
## Step:  AIC=1462.96
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:reading_score                1     2.004 4787.1 1461.2
## - lunch_type:math_score                   1     3.289 4788.4 1461.4
## - transport_means:wkly_study_hours        2    20.963 4806.1 1461.5
## - transport_means:math_score              1     5.331 4790.5 1461.6
## - transport_means:reading_score           1     5.335 4790.5 1461.6
## - test_prep:math_score                    1     8.656 4793.8 1462.0
## - test_prep:is_first_child                1    11.840 4797.0 1462.4
## - test_prep:wkly_study_hours              2    28.959 4814.1 1462.5
## - lunch_type:is_first_child               1    14.019 4799.2 1462.7
## - test_prep:parent_marital_status         3    46.761 4831.9 1462.7
## - ethnic_group:lunch_type                 4    64.686 4849.8 1462.9
## <none>                                                4785.1 1463.0
## - test_prep:transport_means               1    16.292 4801.4 1463.0
## - practice_sport:math_score               2    34.261 4819.4 1463.2
## - ethnic_group:is_first_child             4    70.509 4855.7 1463.6
## - lunch_type:parent_marital_status        3    54.080 4839.2 1463.6
## - gender:math_score                       1    24.168 4809.3 1463.9
## - test_prep:practice_sport                2    41.462 4826.6 1464.0
## - practice_sport:is_first_child           2    41.876 4827.0 1464.1
## - practice_sport:reading_score            2    42.514 4827.7 1464.2
## - parent_educ:reading_score               5    93.442 4878.6 1464.4
## - gender:ethnic_group                     4    77.856 4863.0 1464.5
## + parent_educ:test_prep                   5    67.034 4718.1 1464.6
## + is_first_child:reading_score            1     2.051 4783.1 1464.7
## + gender:lunch_type                       1     1.941 4783.2 1464.7
## + test_prep:reading_score                 1     1.310 4783.8 1464.8
## + is_first_child:math_score               1     1.195 4783.9 1464.8
## + gender:test_prep                        1     0.605 4784.5 1464.9
## + gender:transport_means                  1     0.489 4784.7 1464.9
## + lunch_type:transport_means              1     0.170 4785.0 1464.9
## + is_first_child:transport_means          1     0.157 4785.0 1464.9
## + gender:is_first_child                   1     0.146 4785.0 1464.9
## + lunch_type:test_prep                    1     0.039 4785.1 1465.0
## + wkly_study_hours:reading_score          2    11.793 4773.3 1465.5
## + lunch_type:wkly_study_hours             2    10.195 4774.9 1465.7
## + ethnic_group:wkly_study_hours           8   105.288 4679.9 1465.8
## - parent_educ:lunch_type                  5   106.440 4891.6 1465.9
## + lunch_type:practice_sport               2     8.207 4776.9 1465.9
## - ethnic_group:math_score                 4    90.516 4875.7 1466.0
## + gender:wkly_study_hours                 2     6.681 4778.5 1466.1
## - gender:reading_score                    1    43.560 4828.7 1466.3
## - ethnic_group:test_prep                  4    93.755 4878.9 1466.4
## + practice_sport:transport_means          2     3.823 4781.3 1466.5
## + wkly_study_hours:math_score             2     1.904 4783.2 1466.7
## + gender:parent_marital_status            3    17.636 4767.5 1466.8
## + is_first_child:wkly_study_hours         2     1.396 4783.7 1466.8
## + gender:practice_sport                   2     0.777 4784.4 1466.9
## + parent_marital_status:is_first_child    3    15.015 4770.1 1467.1
## + parent_marital_status:math_score        3    10.405 4774.7 1467.7
## + parent_marital_status:transport_means   3     9.920 4775.2 1467.7
## + ethnic_group:reading_score              4    26.040 4759.1 1467.7
## - parent_educ:math_score                  5   122.116 4907.3 1467.8
## - parent_educ:transport_means             5   123.053 4908.2 1467.9
## + parent_marital_status:reading_score     3     5.362 4779.8 1468.3
## + gender:parent_educ                      5    36.902 4748.2 1468.4
## + ethnic_group:practice_sport             8    83.462 4701.7 1468.6
## + ethnic_group:transport_means            4    18.858 4766.3 1468.6
## + ethnic_group:parent_marital_status     11   124.997 4660.1 1469.3
## + practice_sport:wkly_study_hours         4     6.453 4778.7 1470.2
## - parent_marital_status:wkly_study_hours  6   168.047 4953.2 1471.3
## - math_score:reading_score                1    91.152 4876.3 1472.1
## + parent_marital_status:practice_sport    5     4.286 4780.9 1472.4
## - parent_educ:practice_sport             10   261.469 5046.6 1474.3
## + ethnic_group:parent_educ               20   213.656 4571.5 1476.0
## - parent_educ:is_first_child              5   200.856 4986.0 1477.2
## + parent_educ:wkly_study_hours           10    34.190 4751.0 1478.7
## + parent_educ:parent_marital_status      15    96.087 4689.1 1481.0
## 
## Step:  AIC=1461.2
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:math_score                   1     1.298 4788.4 1459.4
## - transport_means:wkly_study_hours        2    20.461 4807.6 1459.7
## - transport_means:math_score              1     5.126 4792.3 1459.8
## - transport_means:reading_score           1     5.492 4792.6 1459.9
## - test_prep:math_score                    1     8.260 4795.4 1460.2
## - test_prep:is_first_child                1    11.806 4799.0 1460.7
## - test_prep:wkly_study_hours              2    28.216 4815.4 1460.7
## - test_prep:parent_marital_status         3    47.274 4834.4 1461.0
## - ethnic_group:lunch_type                 4    64.214 4851.4 1461.1
## - lunch_type:is_first_child               1    15.264 4802.4 1461.1
## <none>                                                4787.1 1461.2
## - test_prep:transport_means               1    16.638 4803.8 1461.2
## - practice_sport:math_score               2    35.631 4822.8 1461.6
## - lunch_type:parent_marital_status        3    54.208 4841.4 1461.8
## - ethnic_group:is_first_child             4    71.706 4858.9 1462.0
## - gender:math_score                       1    22.652 4809.8 1462.0
## - practice_sport:is_first_child           2    40.687 4827.8 1462.2
## - test_prep:practice_sport                2    41.943 4829.1 1462.3
## - parent_educ:reading_score               5    92.753 4879.9 1462.5
## - practice_sport:reading_score            2    43.632 4830.8 1462.6
## - gender:ethnic_group                     4    78.545 4865.7 1462.8
## + lunch_type:reading_score                1     2.004 4785.1 1463.0
## + is_first_child:reading_score            1     1.670 4785.5 1463.0
## + test_prep:reading_score                 1     1.067 4786.1 1463.1
## + is_first_child:math_score               1     1.040 4786.1 1463.1
## + parent_educ:test_prep                   5    65.065 4722.1 1463.1
## + gender:transport_means                  1     0.574 4786.6 1463.1
## + gender:test_prep                        1     0.401 4786.7 1463.2
## + lunch_type:transport_means              1     0.222 4786.9 1463.2
## + is_first_child:transport_means          1     0.149 4787.0 1463.2
## + lunch_type:test_prep                    1     0.116 4787.0 1463.2
## + gender:is_first_child                   1     0.098 4787.0 1463.2
## + gender:lunch_type                       1     0.004 4787.1 1463.2
## + wkly_study_hours:reading_score          2    11.403 4775.7 1463.8
## + lunch_type:wkly_study_hours             2    10.310 4776.8 1463.9
## + ethnic_group:wkly_study_hours           8   104.720 4682.4 1464.2
## + lunch_type:practice_sport               2     7.829 4779.3 1464.2
## - ethnic_group:math_score                 4    91.289 4878.4 1464.3
## + gender:wkly_study_hours                 2     6.739 4780.4 1464.4
## - gender:reading_score                    1    42.618 4829.8 1464.4
## - ethnic_group:test_prep                  4    93.274 4880.4 1464.6
## + practice_sport:transport_means          2     3.861 4783.3 1464.7
## - parent_educ:lunch_type                  5   111.284 4898.4 1464.8
## + wkly_study_hours:math_score             2     1.857 4785.3 1465.0
## + is_first_child:wkly_study_hours         2     1.478 4785.7 1465.0
## + gender:parent_marital_status            3    17.130 4770.0 1465.1
## + gender:practice_sport                   2     0.601 4786.5 1465.1
## + parent_marital_status:is_first_child    3    16.147 4771.0 1465.2
## + parent_marital_status:math_score        3    10.177 4777.0 1466.0
## + parent_marital_status:transport_means   3    10.032 4777.1 1466.0
## - parent_educ:math_score                  5   121.293 4908.4 1466.0
## + ethnic_group:reading_score              4    25.334 4761.8 1466.1
## - parent_educ:transport_means             5   123.261 4910.4 1466.2
## + parent_marital_status:reading_score     3     4.961 4782.2 1466.6
## + gender:parent_educ                      5    37.078 4750.1 1466.6
## + ethnic_group:transport_means            4    18.962 4768.2 1466.9
## + ethnic_group:practice_sport             8    82.210 4704.9 1467.0
## + ethnic_group:parent_marital_status     11   126.117 4661.0 1467.5
## + practice_sport:wkly_study_hours         4     6.818 4780.3 1468.4
## - parent_marital_status:wkly_study_hours  6   166.713 4953.9 1469.4
## + parent_marital_status:practice_sport    5     4.570 4782.6 1470.6
## - math_score:reading_score                1    99.386 4886.5 1471.3
## - parent_educ:practice_sport             10   261.961 5049.1 1472.6
## + ethnic_group:parent_educ               20   214.826 4572.3 1474.1
## - parent_educ:is_first_child              5   204.064 4991.2 1475.8
## + parent_educ:wkly_study_hours           10    33.581 4753.6 1477.0
## + parent_educ:parent_marital_status      15    97.720 4689.4 1479.0
## 
## Step:  AIC=1459.36
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + transport_means:wkly_study_hours + 
##     transport_means:math_score + transport_means:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - transport_means:wkly_study_hours        2    20.596 4809.0 1457.9
## - transport_means:math_score              1     4.894 4793.3 1458.0
## - transport_means:reading_score           1     5.662 4794.1 1458.1
## - test_prep:math_score                    1     8.998 4797.4 1458.5
## - test_prep:is_first_child                1    11.598 4800.0 1458.8
## - test_prep:wkly_study_hours              2    28.942 4817.4 1458.9
## - test_prep:parent_marital_status         3    46.457 4834.9 1459.1
## - ethnic_group:lunch_type                 4    63.357 4851.8 1459.1
## - lunch_type:is_first_child               1    14.927 4803.4 1459.2
## <none>                                                4788.4 1459.4
## - test_prep:transport_means               1    16.576 4805.0 1459.4
## - practice_sport:math_score               2    36.317 4824.8 1459.8
## - lunch_type:parent_marital_status        3    54.200 4842.6 1460.0
## - gender:math_score                       1    21.879 4810.3 1460.0
## - ethnic_group:is_first_child             4    72.343 4860.8 1460.2
## - practice_sport:is_first_child           2    40.161 4828.6 1460.3
## - test_prep:practice_sport                2    42.186 4830.6 1460.5
## - parent_educ:reading_score               5    92.311 4880.8 1460.6
## - practice_sport:reading_score            2    43.815 4832.3 1460.7
## - gender:ethnic_group                     4    78.266 4866.7 1460.9
## + is_first_child:reading_score            1     1.874 4786.6 1461.1
## + lunch_type:math_score                   1     1.298 4787.1 1461.2
## + test_prep:reading_score                 1     1.230 4787.2 1461.2
## + is_first_child:math_score               1     1.190 4787.3 1461.2
## + gender:transport_means                  1     0.700 4787.7 1461.3
## + gender:test_prep                        1     0.414 4788.0 1461.3
## + lunch_type:transport_means              1     0.235 4788.2 1461.3
## + parent_educ:test_prep                   5    64.646 4723.8 1461.3
## + is_first_child:transport_means          1     0.121 4788.3 1461.3
## + gender:is_first_child                   1     0.090 4788.4 1461.3
## + gender:lunch_type                       1     0.032 4788.4 1461.4
## + lunch_type:reading_score                1     0.013 4788.4 1461.4
## + lunch_type:test_prep                    1     0.007 4788.4 1461.4
## + wkly_study_hours:reading_score          2    11.373 4777.1 1462.0
## + lunch_type:wkly_study_hours             2    11.085 4777.4 1462.0
## + lunch_type:practice_sport               2     7.900 4780.5 1462.4
## + gender:wkly_study_hours                 2     6.968 4781.5 1462.5
## - gender:reading_score                    1    42.447 4830.9 1462.6
## + ethnic_group:wkly_study_hours           8   102.611 4685.8 1462.6
## - parent_educ:lunch_type                  5   110.253 4898.7 1462.8
## - ethnic_group:test_prep                  4    94.023 4882.5 1462.8
## + practice_sport:transport_means          2     3.843 4784.6 1462.9
## - ethnic_group:math_score                 4    95.917 4884.4 1463.1
## + wkly_study_hours:math_score             2     1.846 4786.6 1463.1
## + is_first_child:wkly_study_hours         2     1.442 4787.0 1463.2
## + gender:parent_marital_status            3    16.933 4771.5 1463.3
## + gender:practice_sport                   2     0.552 4787.9 1463.3
## + parent_marital_status:is_first_child    3    15.346 4773.1 1463.5
## - parent_educ:math_score                  5   120.935 4909.4 1464.1
## + ethnic_group:reading_score              4    26.501 4761.9 1464.1
## + parent_marital_status:transport_means   3    10.042 4778.4 1464.1
## + parent_marital_status:math_score        3     9.703 4778.7 1464.2
## - parent_educ:transport_means             5   124.461 4912.9 1464.5
## + gender:parent_educ                      5    37.925 4750.5 1464.7
## + parent_marital_status:reading_score     3     4.955 4783.5 1464.8
## + ethnic_group:transport_means            4    18.948 4769.5 1465.0
## + ethnic_group:practice_sport             8    80.705 4707.7 1465.3
## + ethnic_group:parent_marital_status     11   125.313 4663.1 1465.7
## + practice_sport:wkly_study_hours         4     6.926 4781.5 1466.5
## - parent_marital_status:wkly_study_hours  6   167.095 4955.5 1467.6
## + parent_marital_status:practice_sport    5     4.577 4783.9 1468.8
## - parent_educ:practice_sport             10   264.481 5052.9 1471.1
## - math_score:reading_score                1   121.656 4910.1 1472.2
## + ethnic_group:parent_educ               20   210.232 4578.2 1472.9
## - parent_educ:is_first_child              5   205.050 4993.5 1474.1
## + parent_educ:wkly_study_hours           10    33.164 4755.3 1475.3
## + parent_educ:parent_marital_status      15    96.429 4692.0 1477.4
## 
## Step:  AIC=1457.9
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + transport_means:math_score + 
##     transport_means:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - transport_means:math_score              1     4.513 4813.6 1456.5
## - transport_means:reading_score           1     5.286 4814.3 1456.5
## - test_prep:math_score                    1     7.259 4816.3 1456.8
## - ethnic_group:lunch_type                 4    59.169 4868.2 1457.1
## - test_prep:is_first_child                1    10.441 4819.5 1457.2
## - test_prep:wkly_study_hours              2    26.860 4835.9 1457.2
## - test_prep:parent_marital_status         3    43.513 4852.6 1457.2
## - lunch_type:is_first_child               1    15.607 4824.6 1457.8
## <none>                                                4809.0 1457.9
## - test_prep:transport_means               1    17.638 4826.7 1458.1
## - practice_sport:math_score               2    34.722 4843.8 1458.1
## - ethnic_group:is_first_child             4    70.781 4879.8 1458.5
## - practice_sport:is_first_child           2    39.548 4848.6 1458.7
## - gender:math_score                       1    23.368 4832.4 1458.8
## - test_prep:practice_sport                2    41.104 4850.1 1458.9
## - lunch_type:parent_marital_status        3    58.290 4867.3 1459.0
## - parent_educ:reading_score               5    92.119 4901.2 1459.1
## - practice_sport:reading_score            2    42.543 4851.6 1459.1
## + transport_means:wkly_study_hours        2    20.596 4788.4 1459.4
## + is_first_child:reading_score            1     2.165 4806.9 1459.6
## - gender:ethnic_group                     4    80.253 4889.3 1459.7
## + is_first_child:math_score               1     1.768 4807.3 1459.7
## + lunch_type:math_score                   1     1.434 4807.6 1459.7
## + gender:transport_means                  1     0.997 4808.0 1459.8
## + test_prep:reading_score                 1     0.549 4808.5 1459.8
## + lunch_type:transport_means              1     0.394 4808.6 1459.8
## + is_first_child:transport_means          1     0.096 4808.9 1459.9
## + gender:test_prep                        1     0.066 4809.0 1459.9
## + parent_educ:test_prep                   5    64.825 4744.2 1459.9
## + gender:lunch_type                       1     0.048 4809.0 1459.9
## + lunch_type:test_prep                    1     0.034 4809.0 1459.9
## + gender:is_first_child                   1     0.032 4809.0 1459.9
## + lunch_type:reading_score                1     0.003 4809.0 1459.9
## - parent_educ:lunch_type                  5   103.866 4912.9 1460.5
## - ethnic_group:test_prep                  4    87.390 4896.4 1460.5
## + lunch_type:wkly_study_hours             2    10.822 4798.2 1460.6
## + wkly_study_hours:reading_score          2     8.415 4800.6 1460.9
## + gender:wkly_study_hours                 2     7.867 4801.2 1460.9
## + lunch_type:practice_sport               2     7.191 4801.8 1461.0
## - ethnic_group:math_score                 4    92.414 4901.5 1461.1
## + ethnic_group:wkly_study_hours           8   101.873 4707.2 1461.3
## - gender:reading_score                    1    45.048 4854.1 1461.4
## + practice_sport:transport_means          2     3.892 4805.1 1461.4
## + parent_marital_status:is_first_child    3    19.325 4789.7 1461.5
## + is_first_child:wkly_study_hours         2     1.280 4807.8 1461.7
## + wkly_study_hours:math_score             2     0.764 4808.3 1461.8
## + gender:practice_sport                   2     0.739 4808.3 1461.8
## + gender:parent_marital_status            3    15.791 4793.3 1462.0
## - parent_educ:transport_means             5   119.806 4928.8 1462.4
## + parent_marital_status:transport_means   3    10.883 4798.2 1462.6
## - parent_educ:math_score                  5   121.483 4930.5 1462.6
## + ethnic_group:reading_score              4    25.786 4783.3 1462.7
## + parent_marital_status:math_score        3     8.962 4800.1 1462.8
## + gender:parent_educ                      5    36.787 4772.3 1463.4
## + parent_marital_status:reading_score     3     3.796 4805.2 1463.4
## + ethnic_group:practice_sport             8    83.335 4725.7 1463.6
## + ethnic_group:transport_means            4    18.804 4790.2 1463.6
## + ethnic_group:parent_marital_status     11   123.410 4685.6 1464.6
## + practice_sport:wkly_study_hours         4     6.220 4802.8 1465.1
## - parent_marital_status:wkly_study_hours  6   166.201 4975.2 1465.9
## + parent_marital_status:practice_sport    5     6.264 4802.8 1467.1
## - parent_educ:practice_sport             10   247.478 5056.5 1467.5
## - math_score:reading_score                1   121.323 4930.4 1470.6
## + ethnic_group:parent_educ               20   206.123 4602.9 1472.0
## - parent_educ:is_first_child              5   206.011 5015.1 1472.7
## + parent_educ:wkly_study_hours           10    34.346 4774.7 1473.7
## + parent_educ:parent_marital_status      15    98.255 4710.8 1475.7
## 
## Step:  AIC=1456.45
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + transport_means:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:math_score                    1     7.591 4821.1 1455.4
## - test_prep:parent_marital_status         3    41.589 4855.1 1455.5
## - ethnic_group:lunch_type                 4    58.580 4872.1 1455.6
## - test_prep:wkly_study_hours              2    26.854 4840.4 1455.7
## - test_prep:is_first_child                1    10.520 4824.1 1455.7
## <none>                                                4813.6 1456.5
## - practice_sport:math_score               2    33.160 4846.7 1456.5
## - lunch_type:is_first_child               1    16.898 4830.5 1456.5
## - test_prep:transport_means               1    17.674 4831.2 1456.6
## - ethnic_group:is_first_child             4    69.775 4883.3 1456.9
## - lunch_type:parent_marital_status        3    56.063 4869.6 1457.3
## - practice_sport:is_first_child           2    39.867 4853.4 1457.3
## - parent_educ:reading_score               5    89.613 4903.2 1457.3
## - test_prep:practice_sport                2    40.154 4853.7 1457.3
## - practice_sport:reading_score            2    40.399 4854.0 1457.4
## - gender:math_score                       1    24.567 4838.1 1457.5
## + gender:transport_means                  1     4.693 4808.9 1457.9
## + transport_means:math_score              1     4.513 4809.0 1457.9
## + transport_means:wkly_study_hours        2    20.215 4793.3 1458.0
## - gender:ethnic_group                     4    79.478 4893.0 1458.1
## + is_first_child:reading_score            1     1.990 4811.6 1458.2
## + is_first_child:math_score               1     1.839 4811.7 1458.2
## + parent_educ:test_prep                   5    66.384 4747.2 1458.3
## + lunch_type:math_score                   1     1.192 4812.4 1458.3
## + test_prep:reading_score                 1     0.321 4813.2 1458.4
## + is_first_child:transport_means          1     0.181 4813.4 1458.4
## + gender:lunch_type                       1     0.104 4813.5 1458.4
## + lunch_type:test_prep                    1     0.024 4813.5 1458.5
## + gender:test_prep                        1     0.020 4813.5 1458.5
## + gender:is_first_child                   1     0.009 4813.5 1458.5
## + lunch_type:transport_means              1     0.008 4813.5 1458.5
## + lunch_type:reading_score                1     0.001 4813.6 1458.5
## - ethnic_group:test_prep                  4    84.830 4898.4 1458.8
## + lunch_type:wkly_study_hours             2    11.466 4802.1 1459.0
## - parent_educ:lunch_type                  5   107.528 4921.1 1459.5
## + gender:wkly_study_hours                 2     7.663 4805.9 1459.5
## + lunch_type:practice_sport               2     7.528 4806.0 1459.5
## + wkly_study_hours:reading_score          2     7.137 4806.4 1459.6
## - ethnic_group:math_score                 4    92.922 4906.5 1459.7
## + practice_sport:transport_means          2     3.907 4809.6 1460.0
## + ethnic_group:wkly_study_hours           8    99.355 4714.2 1460.1
## + parent_marital_status:is_first_child    3    18.231 4795.3 1460.2
## - gender:reading_score                    1    47.285 4860.8 1460.2
## + is_first_child:wkly_study_hours         2     1.342 4812.2 1460.3
## + gender:practice_sport                   2     0.748 4812.8 1460.4
## + wkly_study_hours:math_score             2     0.521 4813.0 1460.4
## - transport_means:reading_score           1    49.075 4862.6 1460.4
## + gender:parent_marital_status            3    15.883 4797.7 1460.5
## - parent_educ:transport_means             5   119.457 4933.0 1460.9
## - parent_educ:math_score                  5   120.532 4934.1 1461.0
## + parent_marital_status:transport_means   3    10.541 4803.0 1461.2
## + ethnic_group:reading_score              4    26.349 4787.2 1461.2
## + parent_marital_status:math_score        3     8.130 4805.4 1461.5
## + parent_marital_status:reading_score     3     3.486 4810.1 1462.0
## + gender:parent_educ                      5    35.890 4777.7 1462.0
## + ethnic_group:practice_sport             8    83.259 4730.3 1462.2
## + ethnic_group:transport_means            4    15.849 4797.7 1462.5
## + ethnic_group:parent_marital_status     11   121.875 4691.7 1463.3
## + practice_sport:wkly_study_hours         4     6.472 4807.1 1463.7
## - parent_marital_status:wkly_study_hours  6   166.179 4979.7 1464.5
## + parent_marital_status:practice_sport    5     6.869 4806.7 1465.6
## - parent_educ:practice_sport             10   249.287 5062.8 1466.2
## - math_score:reading_score                1   119.737 4933.3 1469.0
## + ethnic_group:parent_educ               20   206.020 4607.5 1470.6
## - parent_educ:is_first_child              5   208.684 5022.2 1471.5
## + parent_educ:wkly_study_hours           10    34.734 4778.8 1472.2
## + parent_educ:parent_marital_status      15    98.971 4714.6 1474.2
## 
## Step:  AIC=1455.38
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + transport_means:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:parent_marital_status         3    39.544 4860.7 1454.2
## - test_prep:is_first_child                1     9.596 4830.7 1454.5
## - ethnic_group:lunch_type                 4    59.415 4880.6 1454.6
## - lunch_type:is_first_child               1    15.274 4836.4 1455.2
## - test_prep:wkly_study_hours              2    31.812 4853.0 1455.3
## <none>                                                4821.1 1455.4
## - practice_sport:math_score               2    33.078 4854.2 1455.4
## - test_prep:transport_means               1    18.064 4839.2 1455.6
## - ethnic_group:is_first_child             4    70.391 4891.5 1455.9
## - lunch_type:parent_marital_status        3    54.280 4875.4 1456.0
## - practice_sport:is_first_child           2    39.277 4860.4 1456.2
## - test_prep:practice_sport                2    39.461 4860.6 1456.2
## - practice_sport:reading_score            2    40.024 4861.2 1456.3
## + test_prep:math_score                    1     7.591 4813.6 1456.5
## - gender:math_score                       1    25.157 4846.3 1456.5
## + test_prep:reading_score                 1     6.161 4815.0 1456.6
## - parent_educ:reading_score               5    93.907 4915.1 1456.8
## + transport_means:math_score              1     4.846 4816.3 1456.8
## + gender:transport_means                  1     4.577 4816.6 1456.8
## - gender:ethnic_group                     4    78.061 4899.2 1456.9
## + transport_means:wkly_study_hours        2    18.396 4802.7 1457.1
## + parent_educ:test_prep                   5    66.963 4754.2 1457.1
## + lunch_type:math_score                   1     1.827 4819.3 1457.2
## + is_first_child:reading_score            1     1.702 4819.4 1457.2
## + is_first_child:math_score               1     1.387 4819.8 1457.2
## + lunch_type:test_prep                    1     0.880 4820.3 1457.3
## + is_first_child:transport_means          1     0.343 4820.8 1457.3
## + lunch_type:reading_score                1     0.097 4821.0 1457.4
## + gender:test_prep                        1     0.076 4821.1 1457.4
## + gender:is_first_child                   1     0.068 4821.1 1457.4
## + gender:lunch_type                       1     0.041 4821.1 1457.4
## + lunch_type:transport_means              1     0.025 4821.1 1457.4
## - ethnic_group:test_prep                  4    83.143 4904.3 1457.5
## - parent_educ:lunch_type                  5   103.907 4925.1 1458.0
## + lunch_type:wkly_study_hours             2    11.569 4809.6 1458.0
## + gender:wkly_study_hours                 2     7.817 4813.3 1458.4
## + wkly_study_hours:reading_score          2     7.797 4813.3 1458.4
## + lunch_type:practice_sport               2     7.348 4813.8 1458.5
## - ethnic_group:math_score                 4    94.589 4915.7 1458.8
## + ethnic_group:wkly_study_hours           8   100.936 4720.2 1458.9
## + practice_sport:transport_means          2     3.720 4817.4 1458.9
## - gender:reading_score                    1    45.583 4866.7 1458.9
## + parent_marital_status:is_first_child    3    19.341 4801.8 1459.0
## + is_first_child:wkly_study_hours         2     1.392 4819.8 1459.2
## + wkly_study_hours:math_score             2     1.001 4820.1 1459.3
## + gender:practice_sport                   2     0.815 4820.3 1459.3
## + gender:parent_marital_status            3    16.639 4804.5 1459.3
## - transport_means:reading_score           1    53.175 4874.3 1459.8
## - parent_educ:transport_means             5   120.874 4942.0 1460.0
## + parent_marital_status:transport_means   3    11.021 4810.1 1460.0
## + ethnic_group:reading_score              4    26.488 4794.7 1460.1
## + parent_marital_status:math_score        3     6.474 4814.7 1460.6
## + ethnic_group:practice_sport             8    86.638 4734.5 1460.7
## + parent_marital_status:reading_score     3     2.974 4818.2 1461.0
## - parent_educ:math_score                  5   130.004 4951.2 1461.1
## + gender:parent_educ                      5    32.655 4788.5 1461.4
## + ethnic_group:transport_means            4    15.145 4806.0 1461.5
## + ethnic_group:parent_marital_status     11   125.067 4696.1 1461.9
## + practice_sport:wkly_study_hours         4     6.358 4814.8 1462.6
## - parent_marital_status:wkly_study_hours  6   164.431 4985.6 1463.2
## + parent_marital_status:practice_sport    5     6.547 4814.6 1464.6
## - parent_educ:practice_sport             10   252.082 5073.2 1465.5
## + ethnic_group:parent_educ               20   207.951 4613.2 1469.4
## + parent_educ:wkly_study_hours           10    36.367 4784.8 1470.9
## - parent_educ:is_first_child              5   213.866 5035.0 1471.0
## - math_score:reading_score                1   158.103 4979.2 1472.4
## + parent_educ:parent_marital_status      15    99.828 4721.3 1473.0
## 
## Step:  AIC=1454.2
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + test_prep:practice_sport + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:math_score + practice_sport:reading_score + 
##     transport_means:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:is_first_child                1     7.211 4867.9 1453.1
## - ethnic_group:lunch_type                 4    61.611 4922.3 1453.6
## - lunch_type:is_first_child               1    12.104 4872.8 1453.7
## - practice_sport:math_score               2    31.347 4892.0 1454.0
## - test_prep:transport_means               1    15.675 4876.4 1454.1
## <none>                                                4860.7 1454.2
## - test_prep:practice_sport                2    34.169 4894.9 1454.3
## - practice_sport:reading_score            2    37.001 4897.7 1454.7
## - test_prep:wkly_study_hours              2    37.276 4898.0 1454.7
## - practice_sport:is_first_child           2    37.593 4898.3 1454.8
## - ethnic_group:is_first_child             4    72.239 4932.9 1454.9
## - ethnic_group:test_prep                  4    73.992 4934.7 1455.1
## - lunch_type:parent_marital_status        3    57.330 4918.0 1455.1
## - gender:math_score                       1    24.894 4885.6 1455.2
## - gender:ethnic_group                     4    75.399 4936.1 1455.3
## + test_prep:parent_marital_status         3    39.544 4821.1 1455.4
## + test_prep:math_score                    1     5.546 4855.1 1455.5
## + test_prep:reading_score                 1     3.869 4856.8 1455.7
## + gender:transport_means                  1     2.972 4857.7 1455.8
## + transport_means:math_score              1     2.806 4857.9 1455.9
## + is_first_child:reading_score            1     1.518 4859.2 1456.0
## + lunch_type:test_prep                    1     1.297 4859.4 1456.0
## + is_first_child:math_score               1     0.967 4859.7 1456.1
## + lunch_type:math_score                   1     0.829 4859.9 1456.1
## + is_first_child:transport_means          1     0.308 4860.4 1456.2
## + gender:test_prep                        1     0.184 4860.5 1456.2
## + lunch_type:transport_means              1     0.055 4860.6 1456.2
## + lunch_type:reading_score                1     0.021 4860.7 1456.2
## + gender:is_first_child                   1     0.013 4860.7 1456.2
## + gender:lunch_type                       1     0.000 4860.7 1456.2
## + transport_means:wkly_study_hours        2    16.008 4844.7 1456.2
## - parent_educ:lunch_type                  5   101.338 4962.0 1456.4
## + parent_educ:test_prep                   5    59.877 4800.8 1456.9
## + lunch_type:wkly_study_hours             2    10.695 4850.0 1456.9
## - parent_educ:reading_score               5   108.106 4968.8 1457.2
## + lunch_type:practice_sport               2     7.741 4852.9 1457.3
## + parent_marital_status:is_first_child    3    23.240 4837.4 1457.4
## + gender:wkly_study_hours                 2     6.097 4854.6 1457.5
## + wkly_study_hours:reading_score          2     5.406 4855.3 1457.5
## - gender:reading_score                    1    44.730 4905.4 1457.6
## + practice_sport:transport_means          2     3.382 4857.3 1457.8
## + is_first_child:wkly_study_hours         2     2.135 4858.6 1457.9
## + gender:parent_marital_status            3    17.352 4843.3 1458.1
## + gender:practice_sport                   2     0.329 4860.4 1458.2
## + wkly_study_hours:math_score             2     0.258 4860.4 1458.2
## - transport_means:reading_score           1    49.471 4910.2 1458.2
## - ethnic_group:math_score                 4   100.496 4961.2 1458.3
## + ethnic_group:wkly_study_hours           8    93.199 4767.5 1458.8
## - parent_educ:transport_means             5   123.231 4983.9 1459.0
## + parent_marital_status:math_score        3     9.126 4851.6 1459.1
## + parent_marital_status:transport_means   3     6.186 4854.5 1459.5
## + parent_marital_status:reading_score     3     4.568 4856.1 1459.6
## + ethnic_group:reading_score              4    19.362 4841.3 1459.8
## + gender:parent_educ                      5    33.520 4827.2 1460.1
## + ethnic_group:transport_means            4    15.993 4844.7 1460.3
## - parent_educ:math_score                  5   137.452 4998.1 1460.7
## + ethnic_group:parent_marital_status     11   125.976 4734.7 1460.7
## + ethnic_group:practice_sport             8    76.322 4784.4 1460.9
## + practice_sport:wkly_study_hours         4     6.196 4854.5 1461.5
## + parent_marital_status:practice_sport    5     7.488 4853.2 1463.3
## - parent_marital_status:wkly_study_hours  6   187.407 5048.1 1464.5
## - parent_educ:practice_sport             10   269.908 5130.6 1466.1
## + parent_educ:wkly_study_hours           10    40.115 4820.6 1469.3
## + ethnic_group:parent_educ               20   199.011 4661.7 1469.5
## - parent_educ:is_first_child              5   214.728 5075.4 1469.7
## - math_score:reading_score                1   152.633 5013.3 1470.4
## + parent_educ:parent_marital_status      15   102.767 4757.9 1471.6
## 
## Step:  AIC=1453.07
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + test_prep:practice_sport + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:math_score + 
##     practice_sport:reading_score + transport_means:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - practice_sport:math_score               2    29.148 4897.0 1452.6
## - lunch_type:is_first_child               1    13.322 4881.2 1452.7
## - ethnic_group:lunch_type                 4    63.722 4931.6 1452.8
## <none>                                                4867.9 1453.1
## - test_prep:transport_means               1    16.577 4884.5 1453.1
## - test_prep:practice_sport                2    33.778 4901.7 1453.2
## - practice_sport:reading_score            2    35.211 4903.1 1453.3
## - practice_sport:is_first_child           2    36.303 4904.2 1453.5
## - test_prep:wkly_study_hours              2    37.536 4905.4 1453.6
## - gender:ethnic_group                     4    72.661 4940.6 1453.8
## - ethnic_group:is_first_child             4    73.319 4941.2 1453.9
## - lunch_type:parent_marital_status        3    56.600 4924.5 1453.9
## - gender:math_score                       1    24.967 4892.9 1454.1
## + test_prep:is_first_child                1     7.211 4860.7 1454.2
## - ethnic_group:test_prep                  4    76.824 4944.7 1454.3
## + test_prep:math_score                    1     4.972 4862.9 1454.5
## + test_prep:parent_marital_status         3    37.159 4830.7 1454.5
## + test_prep:reading_score                 1     3.577 4864.3 1454.6
## + gender:transport_means                  1     2.940 4865.0 1454.7
## + transport_means:math_score              1     2.877 4865.0 1454.7
## + lunch_type:test_prep                    1     1.145 4866.8 1454.9
## + lunch_type:math_score                   1     0.712 4867.2 1455.0
## + is_first_child:reading_score            1     0.568 4867.3 1455.0
## + is_first_child:math_score               1     0.281 4867.6 1455.0
## + gender:test_prep                        1     0.192 4867.7 1455.0
## + is_first_child:transport_means          1     0.174 4867.7 1455.0
## + gender:is_first_child                   1     0.163 4867.7 1455.0
## + lunch_type:reading_score                1     0.040 4867.9 1455.1
## + gender:lunch_type                       1     0.006 4867.9 1455.1
## + lunch_type:transport_means              1     0.006 4867.9 1455.1
## + transport_means:wkly_study_hours        2    15.218 4852.7 1455.2
## - parent_educ:lunch_type                  5   101.568 4969.5 1455.3
## + lunch_type:wkly_study_hours             2    12.637 4855.3 1455.5
## - parent_educ:reading_score               5   105.068 4973.0 1455.7
## + parent_educ:test_prep                   5    59.441 4808.5 1455.8
## + lunch_type:practice_sport               2     8.120 4859.8 1456.1
## + parent_marital_status:is_first_child    3    24.176 4843.7 1456.1
## + gender:wkly_study_hours                 2     5.523 4862.4 1456.4
## - gender:reading_score                    1    44.231 4912.1 1456.4
## + wkly_study_hours:reading_score          2     4.576 4863.3 1456.5
## + practice_sport:transport_means          2     3.588 4864.3 1456.6
## + is_first_child:wkly_study_hours         2     2.884 4865.0 1456.7
## - ethnic_group:math_score                 4    99.032 4966.9 1457.0
## + gender:practice_sport                   2     0.272 4867.6 1457.0
## + wkly_study_hours:math_score             2     0.175 4867.7 1457.0
## + gender:parent_marital_status            3    16.474 4851.4 1457.1
## - transport_means:reading_score           1    50.435 4918.3 1457.2
## + ethnic_group:wkly_study_hours           8    92.156 4775.7 1457.8
## + parent_marital_status:math_score        3    10.117 4857.8 1457.8
## - parent_educ:transport_means             5   124.317 4992.2 1458.0
## + parent_marital_status:transport_means   3     5.830 4862.1 1458.4
## + parent_marital_status:reading_score     3     5.458 4862.4 1458.4
## + ethnic_group:reading_score              4    17.941 4850.0 1458.9
## + gender:parent_educ                      5    34.109 4833.8 1458.9
## + ethnic_group:transport_means            4    15.277 4852.6 1459.2
## - parent_educ:math_score                  5   135.174 5003.1 1459.2
## + ethnic_group:practice_sport             8    75.787 4792.1 1459.8
## + ethnic_group:parent_marital_status     11   121.039 4746.9 1460.2
## + practice_sport:wkly_study_hours         4     6.509 4861.4 1460.3
## + parent_marital_status:practice_sport    5     7.551 4860.3 1462.2
## - parent_marital_status:wkly_study_hours  6   186.214 5054.1 1463.2
## - parent_educ:practice_sport             10   266.999 5134.9 1464.6
## + parent_educ:wkly_study_hours           10    38.849 4829.1 1468.3
## + ethnic_group:parent_educ               20   198.698 4669.2 1468.5
## - parent_educ:is_first_child              5   214.875 5082.8 1468.6
## - math_score:reading_score                1   153.701 5021.6 1469.4
## + parent_educ:parent_marital_status      15   106.785 4761.1 1470.0
## 
## Step:  AIC=1452.6
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + test_prep:practice_sport + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:reading_score + 
##     transport_means:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - practice_sport:reading_score            2     8.869 4905.9 1449.7
## - ethnic_group:lunch_type                 4    59.637 4956.7 1451.7
## - lunch_type:is_first_child               1    13.679 4910.7 1452.2
## <none>                                                4897.0 1452.6
## - test_prep:practice_sport                2    33.717 4930.8 1452.6
## - test_prep:transport_means               1    17.390 4914.4 1452.7
## - gender:ethnic_group                     4    68.000 4965.0 1452.7
## - ethnic_group:is_first_child             4    69.316 4966.4 1452.9
## + practice_sport:math_score               2    29.148 4867.9 1453.1
## - gender:math_score                       1    20.844 4917.9 1453.1
## - practice_sport:is_first_child           2    38.263 4935.3 1453.2
## - test_prep:wkly_study_hours              2    38.557 4935.6 1453.2
## - parent_educ:lunch_type                  5    92.222 4989.3 1453.6
## - lunch_type:parent_marital_status        3    58.739 4955.8 1453.6
## - ethnic_group:test_prep                  4    77.160 4974.2 1453.8
## + test_prep:is_first_child                1     5.012 4892.0 1454.0
## + test_prep:math_score                    1     4.975 4892.1 1454.0
## + test_prep:reading_score                 1     4.122 4892.9 1454.1
## + test_prep:parent_marital_status         3    35.893 4861.2 1454.3
## + gender:transport_means                  1     2.097 4895.0 1454.3
## + transport_means:math_score              1     1.771 4895.3 1454.4
## + lunch_type:math_score                   1     1.278 4895.8 1454.4
## + lunch_type:test_prep                    1     1.222 4895.8 1454.5
## + is_first_child:reading_score            1     0.351 4896.7 1454.5
## + is_first_child:math_score               1     0.191 4896.9 1454.6
## + gender:test_prep                        1     0.135 4896.9 1454.6
## + is_first_child:transport_means          1     0.127 4896.9 1454.6
## + gender:is_first_child                   1     0.099 4896.9 1454.6
## + lunch_type:reading_score                1     0.065 4897.0 1454.6
## + gender:lunch_type                       1     0.043 4897.0 1454.6
## + lunch_type:transport_means              1     0.010 4897.0 1454.6
## + gender:practice_sport                   2    15.618 4881.4 1454.7
## + transport_means:wkly_study_hours        2    14.286 4882.8 1454.9
## + parent_educ:test_prep                   5    63.077 4834.0 1455.0
## - parent_educ:reading_score               5   104.299 5001.3 1455.0
## - gender:reading_score                    1    37.077 4934.1 1455.0
## + lunch_type:wkly_study_hours             2    11.544 4885.5 1455.2
## - ethnic_group:math_score                 4    90.416 4987.5 1455.4
## + parent_marital_status:is_first_child    3    24.139 4872.9 1455.7
## + gender:wkly_study_hours                 2     5.991 4891.1 1455.9
## + lunch_type:practice_sport               2     5.753 4891.3 1455.9
## + wkly_study_hours:reading_score          2     4.962 4892.1 1456.0
## + practice_sport:transport_means          2     3.920 4893.1 1456.1
## + is_first_child:wkly_study_hours         2     3.762 4893.3 1456.1
## + wkly_study_hours:math_score             2     0.407 4896.6 1456.5
## + gender:parent_marital_status            3    15.789 4881.3 1456.7
## - transport_means:reading_score           1    52.184 4949.2 1456.8
## - parent_educ:transport_means             5   123.530 5020.6 1457.3
## + parent_marital_status:math_score        3     7.827 4889.2 1457.7
## + ethnic_group:wkly_study_hours           8    89.619 4807.4 1457.7
## + parent_marital_status:transport_means   3     5.465 4891.6 1457.9
## + ethnic_group:reading_score              4    21.802 4875.2 1458.0
## - parent_educ:math_score                  5   130.420 5027.5 1458.1
## + parent_marital_status:reading_score     3     4.064 4893.0 1458.1
## + gender:parent_educ                      5    34.493 4862.6 1458.4
## + ethnic_group:transport_means            4    15.111 4881.9 1458.8
## + practice_sport:wkly_study_hours         4    12.251 4884.8 1459.1
## + ethnic_group:parent_marital_status     11   120.503 4776.5 1459.9
## + ethnic_group:practice_sport             8    63.689 4833.4 1460.9
## - parent_marital_status:wkly_study_hours  6   176.076 5073.1 1461.4
## + parent_marital_status:practice_sport    5     8.508 4888.5 1461.6
## - parent_educ:practice_sport             10   256.786 5153.8 1462.8
## + ethnic_group:parent_educ               20   213.140 4683.9 1466.3
## - parent_educ:is_first_child              5   203.324 5100.4 1466.6
## + parent_educ:wkly_study_hours           10    45.812 4851.2 1467.0
## + parent_educ:parent_marital_status      15   110.433 4786.6 1469.1
## - math_score:reading_score                1   160.689 5057.7 1469.7
## 
## Step:  AIC=1449.66
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + test_prep:practice_sport + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + transport_means:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:lunch_type                 4    57.590 4963.5 1448.5
## - test_prep:practice_sport                2    29.524 4935.4 1449.2
## - lunch_type:is_first_child               1    14.122 4920.0 1449.4
## - gender:ethnic_group                     4    64.897 4970.8 1449.4
## <none>                                                4905.9 1449.7
## - test_prep:transport_means               1    16.979 4922.9 1449.7
## - gender:math_score                       1    20.576 4926.5 1450.1
## - ethnic_group:is_first_child             4    73.185 4979.1 1450.4
## - test_prep:wkly_study_hours              2    39.617 4945.5 1450.4
## - practice_sport:is_first_child           2    39.775 4945.7 1450.4
## - parent_educ:lunch_type                  5    91.564 4997.5 1450.6
## - lunch_type:parent_marital_status        3    59.326 4965.2 1450.8
## + test_prep:is_first_child                1     5.557 4900.4 1451.0
## - ethnic_group:test_prep                  4    79.123 4985.0 1451.1
## + test_prep:math_score                    1     4.469 4901.4 1451.1
## + test_prep:reading_score                 1     3.727 4902.2 1451.2
## + gender:practice_sport                   2    19.349 4886.6 1451.3
## + test_prep:parent_marital_status         3    35.592 4870.3 1451.4
## + gender:transport_means                  1     1.869 4904.0 1451.4
## + lunch_type:test_prep                    1     1.383 4904.5 1451.5
## + transport_means:math_score              1     1.352 4904.6 1451.5
## + lunch_type:math_score                   1     0.976 4904.9 1451.5
## + is_first_child:reading_score            1     0.445 4905.5 1451.6
## + is_first_child:math_score               1     0.275 4905.6 1451.6
## + lunch_type:reading_score                1     0.152 4905.8 1451.7
## + gender:test_prep                        1     0.095 4905.8 1451.7
## + is_first_child:transport_means          1     0.036 4905.9 1451.7
## + gender:lunch_type                       1     0.026 4905.9 1451.7
## + gender:is_first_child                   1     0.025 4905.9 1451.7
## + lunch_type:transport_means              1     0.008 4905.9 1451.7
## + transport_means:wkly_study_hours        2    15.140 4890.8 1451.8
## + parent_educ:test_prep                   5    63.990 4841.9 1451.9
## - gender:reading_score                    1    36.459 4942.4 1452.0
## + lunch_type:wkly_study_hours             2    11.010 4894.9 1452.3
## - parent_educ:reading_score               5   106.834 5012.8 1452.4
## + parent_marital_status:is_first_child    3    27.076 4878.8 1452.4
## + practice_sport:reading_score            2     8.869 4897.0 1452.6
## + lunch_type:practice_sport               2     7.197 4898.7 1452.8
## + gender:wkly_study_hours                 2     6.437 4899.5 1452.9
## + wkly_study_hours:reading_score          2     5.963 4900.0 1453.0
## - ethnic_group:math_score                 4    94.736 5000.7 1453.0
## + is_first_child:wkly_study_hours         2     4.307 4901.6 1453.2
## + practice_sport:transport_means          2     3.350 4902.6 1453.3
## + practice_sport:math_score               2     2.806 4903.1 1453.3
## + wkly_study_hours:math_score             2     0.555 4905.4 1453.6
## + gender:parent_marital_status            3    14.669 4891.2 1453.9
## - transport_means:reading_score           1    52.264 4958.2 1453.9
## - parent_educ:transport_means             5   120.929 5026.8 1454.0
## + parent_marital_status:math_score        3     8.074 4897.8 1454.7
## + ethnic_group:wkly_study_hours           8    89.289 4816.6 1454.8
## + parent_marital_status:transport_means   3     5.066 4900.9 1455.0
## + ethnic_group:reading_score              4    21.252 4884.7 1455.1
## + parent_marital_status:reading_score     3     4.131 4901.8 1455.2
## + gender:parent_educ                      5    34.914 4871.0 1455.5
## - parent_educ:math_score                  5   133.908 5039.8 1455.5
## + ethnic_group:transport_means            4    16.936 4889.0 1455.6
## + practice_sport:wkly_study_hours         4    10.966 4895.0 1456.3
## + ethnic_group:parent_marital_status     11   115.542 4790.4 1457.6
## + ethnic_group:practice_sport             8    59.421 4846.5 1458.5
## + parent_marital_status:practice_sport    5     9.100 4896.8 1458.6
## - parent_marital_status:wkly_study_hours  6   178.107 5084.0 1458.7
## - parent_educ:practice_sport             10   275.711 5181.6 1461.9
## + ethnic_group:parent_educ               20   211.776 4694.1 1463.6
## - parent_educ:is_first_child              5   209.854 5115.8 1464.4
## + parent_educ:wkly_study_hours           10    42.304 4863.6 1464.5
## + parent_educ:parent_marital_status      15   112.142 4793.8 1466.0
## - math_score:reading_score                1   164.201 5070.1 1467.1
## 
## Step:  AIC=1448.55
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     transport_means:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:practice_sport                2    29.535 4993.0 1448.0
## - test_prep:transport_means               1    12.947 4976.5 1448.1
## - test_prep:wkly_study_hours              2    33.345 4996.9 1448.5
## <none>                                                4963.5 1448.5
## - lunch_type:is_first_child               1    17.949 4981.5 1448.7
## - gender:math_score                       1    18.395 4981.9 1448.7
## - gender:ethnic_group                     4    71.565 5035.1 1449.0
## - practice_sport:is_first_child           2    38.657 5002.2 1449.1
## - parent_educ:lunch_type                  5    91.280 5054.8 1449.3
## - lunch_type:parent_marital_status        3    58.011 5021.5 1449.4
## - ethnic_group:math_score                 4    77.101 5040.6 1449.6
## + test_prep:is_first_child                1     7.483 4956.0 1449.7
## + ethnic_group:lunch_type                 4    57.590 4905.9 1449.7
## - ethnic_group:is_first_child             4    77.289 5040.8 1449.7
## - parent_educ:reading_score               5    94.830 5058.3 1449.7
## + test_prep:math_score                    1     5.019 4958.5 1450.0
## + gender:practice_sport                   2    21.112 4942.4 1450.0
## + test_prep:parent_marital_status         3    37.109 4926.4 1450.1
## + test_prep:reading_score                 1     3.124 4960.4 1450.2
## + gender:transport_means                  1     2.077 4961.4 1450.3
## + lunch_type:test_prep                    1     1.475 4962.0 1450.4
## + transport_means:math_score              1     1.278 4962.2 1450.4
## + parent_educ:test_prep                   5    67.894 4895.6 1450.4
## - gender:reading_score                    1    32.886 4996.4 1450.5
## + lunch_type:reading_score                1     0.352 4963.2 1450.5
## + lunch_type:math_score                   1     0.215 4963.3 1450.5
## + is_first_child:transport_means          1     0.173 4963.3 1450.5
## + gender:test_prep                        1     0.140 4963.4 1450.5
## + is_first_child:math_score               1     0.088 4963.4 1450.5
## + gender:is_first_child                   1     0.066 4963.4 1450.5
## + lunch_type:transport_means              1     0.060 4963.4 1450.5
## + is_first_child:reading_score            1     0.032 4963.5 1450.5
## + gender:lunch_type                       1     0.017 4963.5 1450.5
## + lunch_type:wkly_study_hours             2    14.109 4949.4 1450.9
## - ethnic_group:test_prep                  4    87.602 5051.1 1450.9
## + transport_means:wkly_study_hours        2    12.024 4951.5 1451.1
## + parent_marital_status:is_first_child    3    28.559 4934.9 1451.2
## - parent_educ:transport_means             5   110.911 5074.4 1451.6
## + practice_sport:reading_score            2     6.822 4956.7 1451.7
## + gender:wkly_study_hours                 2     5.633 4957.9 1451.9
## + lunch_type:practice_sport               2     4.928 4958.6 1452.0
## + practice_sport:transport_means          2     3.077 4960.4 1452.2
## + is_first_child:wkly_study_hours         2     2.765 4960.7 1452.2
## + practice_sport:math_score               2     2.680 4960.8 1452.2
## + wkly_study_hours:reading_score          2     2.570 4960.9 1452.2
## - transport_means:reading_score           1    48.284 5011.8 1452.3
## + wkly_study_hours:math_score             2     0.026 4963.5 1452.5
## - parent_educ:math_score                  5   121.085 5084.6 1452.8
## + gender:parent_marital_status            3    13.852 4949.7 1452.9
## + ethnic_group:wkly_study_hours           8    93.425 4870.1 1453.3
## + parent_marital_status:transport_means   3     7.674 4955.8 1453.6
## + parent_marital_status:math_score        3     5.929 4957.6 1453.8
## + gender:parent_educ                      5    38.586 4924.9 1454.0
## + parent_marital_status:reading_score     3     2.686 4960.8 1454.2
## + practice_sport:wkly_study_hours         4    12.280 4951.2 1455.1
## + ethnic_group:transport_means            4    11.772 4951.7 1455.2
## + ethnic_group:reading_score              4    11.538 4952.0 1455.2
## + parent_marital_status:practice_sport    5    10.208 4953.3 1457.3
## - parent_marital_status:wkly_study_hours  6   181.841 5145.3 1457.8
## + ethnic_group:practice_sport             8    55.921 4907.6 1457.9
## + ethnic_group:parent_marital_status     11    99.162 4864.3 1458.6
## - parent_educ:practice_sport             10   263.191 5226.7 1459.0
## + parent_educ:wkly_study_hours           10    49.114 4914.4 1462.7
## - parent_educ:is_first_child              5   213.726 5177.2 1463.4
## + ethnic_group:parent_educ               20   206.252 4757.3 1463.5
## - math_score:reading_score                1   162.772 5126.3 1465.6
## + parent_educ:parent_marital_status      15   103.300 4860.2 1466.1
## 
## Step:  AIC=1448.05
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     transport_means:reading_score + math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:transport_means               1    13.693 5006.7 1447.7
## <none>                                                4993.0 1448.0
## - test_prep:wkly_study_hours              2    34.710 5027.8 1448.1
## - gender:math_score                       1    18.873 5011.9 1448.3
## - gender:ethnic_group                     4    70.139 5063.2 1448.3
## - lunch_type:is_first_child               1    19.178 5012.2 1448.3
## - practice_sport:is_first_child           2    36.589 5029.6 1448.4
## + test_prep:practice_sport                2    29.535 4963.5 1448.5
## - lunch_type:parent_marital_status        3    55.552 5048.6 1448.6
## - parent_educ:reading_score               5    93.524 5086.6 1449.0
## - ethnic_group:math_score                 4    77.680 5070.7 1449.2
## + ethnic_group:lunch_type                 4    57.601 4935.4 1449.2
## - ethnic_group:is_first_child             4    78.091 5071.1 1449.2
## + test_prep:is_first_child                1     6.668 4986.4 1449.3
## - parent_educ:lunch_type                  5    96.537 5089.6 1449.3
## + test_prep:math_score                    1     4.513 4988.5 1449.5
## + gender:practice_sport                   2    21.082 4972.0 1449.5
## + test_prep:reading_score                 1     3.621 4989.4 1449.6
## + parent_educ:test_prep                   5    70.184 4922.9 1449.7
## - ethnic_group:test_prep                  4    82.851 5075.9 1449.8
## + gender:transport_means                  1     2.223 4990.8 1449.8
## + lunch_type:test_prep                    1     1.819 4991.2 1449.8
## + transport_means:math_score              1     1.120 4991.9 1449.9
## - gender:reading_score                    1    32.843 5025.9 1449.9
## + lunch_type:reading_score                1     0.433 4992.6 1450.0
## + is_first_child:math_score               1     0.394 4992.6 1450.0
## + lunch_type:math_score                   1     0.217 4992.8 1450.0
## + is_first_child:transport_means          1     0.183 4992.9 1450.0
## + gender:test_prep                        1     0.112 4992.9 1450.0
## + is_first_child:reading_score            1     0.104 4992.9 1450.0
## + lunch_type:transport_means              1     0.009 4993.0 1450.0
## + gender:lunch_type                       1     0.008 4993.0 1450.0
## + gender:is_first_child                   1     0.008 4993.0 1450.0
## + test_prep:parent_marital_status         3    33.480 4959.6 1450.1
## + lunch_type:wkly_study_hours             2    12.191 4980.9 1450.6
## + transport_means:wkly_study_hours        2    12.077 4981.0 1450.6
## + parent_marital_status:is_first_child    3    23.996 4969.0 1451.2
## + practice_sport:math_score               2     5.780 4987.3 1451.4
## + gender:wkly_study_hours                 2     5.256 4987.8 1451.4
## + lunch_type:practice_sport               2     5.099 4987.9 1451.5
## + practice_sport:transport_means          2     4.319 4988.7 1451.5
## + practice_sport:reading_score            2     3.641 4989.4 1451.6
## + is_first_child:wkly_study_hours         2     3.047 4990.0 1451.7
## - parent_educ:math_score                  5   117.660 5110.7 1451.8
## - transport_means:reading_score           1    49.010 5042.1 1451.8
## + wkly_study_hours:reading_score          2     1.884 4991.2 1451.8
## - parent_educ:transport_means             5   118.034 5111.1 1451.8
## + wkly_study_hours:math_score             2     0.113 4992.9 1452.0
## + gender:parent_marital_status            3    10.576 4982.5 1452.8
## + parent_marital_status:transport_means   3     8.311 4984.7 1453.1
## + ethnic_group:wkly_study_hours           8    91.953 4901.1 1453.1
## + gender:parent_educ                      5    40.708 4952.3 1453.2
## + parent_marital_status:math_score        3     5.310 4987.7 1453.4
## + parent_marital_status:reading_score     3     2.543 4990.5 1453.8
## + practice_sport:wkly_study_hours         4    16.272 4976.8 1454.1
## + ethnic_group:transport_means            4    13.498 4979.5 1454.5
## + ethnic_group:reading_score              4     8.447 4984.6 1455.0
## - parent_marital_status:wkly_study_hours  6   173.095 5166.1 1456.2
## + parent_marital_status:practice_sport    5     8.998 4984.0 1457.0
## + ethnic_group:practice_sport             8    54.476 4938.6 1457.6
## + ethnic_group:parent_marital_status     11    98.173 4894.9 1458.3
## - parent_educ:practice_sport             10   282.569 5275.6 1460.5
## + parent_educ:wkly_study_hours           10    51.053 4942.0 1462.0
## + ethnic_group:parent_educ               20   212.063 4781.0 1462.4
## - parent_educ:is_first_child              5   222.902 5215.9 1463.8
## - math_score:reading_score                1   159.018 5152.1 1464.5
## + parent_educ:parent_marital_status      15   103.415 4889.6 1465.7
## 
## Step:  AIC=1447.67
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + math_score + reading_score + 
##     gender:ethnic_group + gender:math_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:math_score + 
##     parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score + 
##     lunch_type:parent_marital_status + lunch_type:is_first_child + 
##     test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + transport_means:reading_score + 
##     math_score:reading_score
## 
##                                          Df Sum of Sq    RSS    AIC
## <none>                                                5006.7 1447.7
## - lunch_type:is_first_child               1    17.101 5023.8 1447.7
## - test_prep:wkly_study_hours              2    35.503 5042.2 1447.8
## - gender:ethnic_group                     4    71.201 5077.9 1448.0
## - gender:math_score                       1    20.172 5026.9 1448.0
## + test_prep:transport_means               1    13.693 4993.0 1448.0
## + test_prep:practice_sport                2    30.281 4976.5 1448.1
## - lunch_type:parent_marital_status        3    54.991 5061.7 1448.1
## - practice_sport:is_first_child           2    38.826 5045.6 1448.2
## - ethnic_group:math_score                 4    75.283 5082.0 1448.5
## - parent_educ:reading_score               5    95.071 5101.8 1448.8
## + test_prep:is_first_child                1     7.284 4999.5 1448.8
## - ethnic_group:is_first_child             4    79.586 5086.3 1449.0
## + test_prep:math_score                    1     4.945 5001.8 1449.1
## + test_prep:reading_score                 1     4.470 5002.3 1449.1
## + gender:practice_sport                   2    20.819 4985.9 1449.2
## + ethnic_group:lunch_type                 4    53.577 4953.2 1449.3
## + lunch_type:test_prep                    1     1.784 5005.0 1449.5
## + transport_means:math_score              1     1.148 5005.6 1449.5
## + gender:transport_means                  1     1.115 5005.6 1449.5
## - gender:reading_score                    1    33.121 5039.9 1449.6
## + parent_educ:test_prep                   5    68.199 4938.5 1449.6
## + lunch_type:reading_score                1     0.621 5006.1 1449.6
## - parent_educ:lunch_type                  5   102.424 5109.2 1449.6
## + is_first_child:math_score               1     0.284 5006.5 1449.6
## + lunch_type:math_score                   1     0.139 5006.6 1449.7
## + is_first_child:reading_score            1     0.069 5006.7 1449.7
## + lunch_type:transport_means              1     0.067 5006.7 1449.7
## + is_first_child:transport_means          1     0.042 5006.7 1449.7
## + gender:lunch_type                       1     0.023 5006.7 1449.7
## + gender:is_first_child                   1     0.010 5006.7 1449.7
## + gender:test_prep                        1     0.009 5006.7 1449.7
## + test_prep:parent_marital_status         3    31.004 4975.7 1450.0
## + lunch_type:wkly_study_hours             2    13.040 4993.7 1450.1
## - ethnic_group:test_prep                  4    89.967 5096.7 1450.2
## + transport_means:wkly_study_hours        2    12.528 4994.2 1450.2
## - transport_means:reading_score           1    41.160 5047.9 1450.5
## - parent_educ:transport_means             5   111.350 5118.1 1450.6
## + parent_marital_status:is_first_child    3    25.163 4981.6 1450.7
## + gender:wkly_study_hours                 2     6.146 5000.6 1450.9
## + practice_sport:math_score               2     5.843 5000.9 1451.0
## + lunch_type:practice_sport               2     5.460 5001.3 1451.0
## + practice_sport:transport_means          2     4.037 5002.7 1451.2
## + wkly_study_hours:reading_score          2     3.307 5003.4 1451.3
## + practice_sport:reading_score            2     3.166 5003.6 1451.3
## + is_first_child:wkly_study_hours         2     2.699 5004.0 1451.3
## - parent_educ:math_score                  5   120.038 5126.8 1451.6
## + wkly_study_hours:math_score             2     0.164 5006.6 1451.7
## + gender:parent_marital_status            3    11.505 4995.2 1452.3
## + gender:parent_educ                      5    44.891 4961.8 1452.3
## + parent_marital_status:transport_means   3     7.778 4999.0 1452.8
## + parent_marital_status:math_score        3     4.936 5001.8 1453.1
## + ethnic_group:wkly_study_hours           8    88.359 4918.4 1453.2
## + parent_marital_status:reading_score     3     1.952 5004.8 1453.4
## + practice_sport:wkly_study_hours         4    14.210 4992.5 1454.0
## + ethnic_group:transport_means            4    11.725 4995.0 1454.3
## + ethnic_group:reading_score              4     8.036 4998.7 1454.7
## - parent_marital_status:wkly_study_hours  6   173.417 5180.2 1455.8
## + parent_marital_status:practice_sport    5     8.201 4998.5 1456.7
## + ethnic_group:practice_sport             8    54.682 4952.1 1457.2
## + ethnic_group:parent_marital_status     11   101.721 4905.0 1457.6
## - parent_educ:practice_sport             10   274.151 5280.9 1459.1
## + parent_educ:wkly_study_hours           10    53.714 4953.0 1461.3
## + ethnic_group:parent_educ               20   210.965 4795.8 1462.3
## - math_score:reading_score                1   155.833 5162.6 1463.8
## - parent_educ:is_first_child              5   226.710 5233.4 1463.8
## + parent_educ:parent_marital_status      15   103.775 4903.0 1465.3
summary(stepwise_model_write2)
## 
## Call:
## lm(formula = writing_score ~ gender + ethnic_group + parent_educ + 
##     lunch_type + test_prep + parent_marital_status + practice_sport + 
##     is_first_child + transport_means + wkly_study_hours + math_score + 
##     reading_score + gender:ethnic_group + gender:math_score + 
##     gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status + 
##     lunch_type:is_first_child + test_prep:wkly_study_hours + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     transport_means:reading_score + math_score:reading_score, 
##     data = df_4_mdl_write2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.9657 -2.0030  0.0213  1.8692  7.4929 
## 
## Coefficients:
##                                                          Estimate Std. Error
## (Intercept)                                             9.6445037  4.5127588
## gendermale                                             -6.5114045  1.7135103
## ethnic_groupgroup B                                    -8.3857922  3.2849149
## ethnic_groupgroup C                                    -6.0166328  3.1934620
## ethnic_groupgroup D                                    -2.5744505  3.2587321
## ethnic_groupgroup E                                    -5.3119146  3.7496070
## parent_educbachelor's degree                           -2.9973857  3.1823772
## parent_educhigh school                                 -1.7838156  2.7248502
## parent_educmaster's degree                              6.1140140  3.6072864
## parent_educsome college                                -3.1020032  2.5960042
## parent_educsome high school                            -1.4232574  2.5056988
## lunch_typestandard                                      0.4477869  1.0482590
## test_prepnone                                          -4.3303001  1.2882595
## parent_marital_statusmarried                           -1.7237774  0.9647154
## parent_marital_statussingle                            -1.2636368  1.0556089
## parent_marital_statuswidowed                           -1.0260639  2.5355813
## practice_sportregularly                                 2.6275926  1.2818376
## practice_sportsometimes                                 2.0495873  1.2638189
## is_first_childyes                                      -1.9449244  1.5377155
## transport_meansschool_bus                              -3.0246990  1.5733964
## wkly_study_hours> 10                                   -1.5274396  1.3217426
## wkly_study_hours10-May                                 -3.5627989  0.9998964
## math_score                                              0.4380746  0.0684638
## reading_score                                           0.6616880  0.0545786
## gendermale:ethnic_groupgroup B                         -1.9698990  1.1594194
## gendermale:ethnic_groupgroup C                         -1.9477103  1.1268362
## gendermale:ethnic_groupgroup D                         -0.7023720  1.1209408
## gendermale:ethnic_groupgroup E                         -2.3988290  1.2795874
## gendermale:math_score                                  -0.0617195  0.0436166
## gendermale:reading_score                                0.0832689  0.0459233
## ethnic_groupgroup B:test_prepnone                       1.3387366  1.3136969
## ethnic_groupgroup C:test_prepnone                      -0.1980783  1.2648345
## ethnic_groupgroup D:test_prepnone                      -1.2194398  1.2755736
## ethnic_groupgroup E:test_prepnone                       0.3828767  1.3501492
## ethnic_groupgroup B:is_first_childyes                   2.0753697  1.2206728
## ethnic_groupgroup C:is_first_childyes                   3.1156547  1.1453637
## ethnic_groupgroup D:is_first_childyes                   2.0611699  1.1686539
## ethnic_groupgroup E:is_first_childyes                   2.5880354  1.2645035
## ethnic_groupgroup B:math_score                          0.1096732  0.0423353
## ethnic_groupgroup C:math_score                          0.0878905  0.0403791
## ethnic_groupgroup D:math_score                          0.0702058  0.0413579
## ethnic_groupgroup E:math_score                          0.0638520  0.0463740
## parent_educbachelor's degree:lunch_typestandard        -0.6844103  1.1895771
## parent_educhigh school:lunch_typestandard               0.9483806  0.9401266
## parent_educmaster's degree:lunch_typestandard          -0.4804909  1.4903982
## parent_educsome college:lunch_typestandard              2.3864722  0.9473051
## parent_educsome high school:lunch_typestandard          0.5992191  0.9902033
## parent_educbachelor's degree:practice_sportregularly    2.1457242  1.7035570
## parent_educhigh school:practice_sportregularly          1.8746993  1.4992648
## parent_educmaster's degree:practice_sportregularly     -0.5190348  2.0827015
## parent_educsome college:practice_sportregularly         0.4547936  1.5123630
## parent_educsome high school:practice_sportregularly    -1.0613776  1.4964049
## parent_educbachelor's degree:practice_sportsometimes    0.6005963  1.6169653
## parent_educhigh school:practice_sportsometimes          1.1756757  1.4278871
## parent_educmaster's degree:practice_sportsometimes     -2.4834386  1.7644790
## parent_educsome college:practice_sportsometimes         1.9047387  1.4769477
## parent_educsome high school:practice_sportsometimes    -2.9731665  1.4119638
## parent_educbachelor's degree:is_first_childyes          2.6916133  1.0850313
## parent_educhigh school:is_first_childyes                1.9545744  0.9255417
## parent_educmaster's degree:is_first_childyes           -2.4678171  1.4325959
## parent_educsome college:is_first_childyes               2.8513272  0.9320346
## parent_educsome high school:is_first_childyes           2.1110432  0.9163858
## parent_educbachelor's degree:transport_meansschool_bus  0.2283265  1.0706439
## parent_educhigh school:transport_meansschool_bus        1.0958791  0.8999995
## parent_educmaster's degree:transport_meansschool_bus   -0.9471291  1.3220984
## parent_educsome college:transport_meansschool_bus      -1.0455703  0.9065922
## parent_educsome high school:transport_meansschool_bus   1.6285776  0.9162492
## parent_educbachelor's degree:math_score                -0.0804471  0.0600067
## parent_educhigh school:math_score                      -0.0625786  0.0472331
## parent_educmaster's degree:math_score                   0.1435242  0.0846319
## parent_educsome college:math_score                     -0.0546444  0.0495927
## parent_educsome high school:math_score                 -0.1092178  0.0480917
## parent_educbachelor's degree:reading_score              0.0957272  0.0623827
## parent_educhigh school:reading_score                    0.0116011  0.0509301
## parent_educmaster's degree:reading_score               -0.1208817  0.0875665
## parent_educsome college:reading_score                   0.0440348  0.0507576
## parent_educsome high school:reading_score               0.0923790  0.0507521
## lunch_typestandard:parent_marital_statusmarried        -0.0654145  0.8403535
## lunch_typestandard:parent_marital_statussingle         -1.6134573  0.9536181
## lunch_typestandard:parent_marital_statuswidowed        -1.7849309  2.2385991
## lunch_typestandard:is_first_childyes                   -0.8390022  0.6439557
## test_prepnone:wkly_study_hours> 10                      0.8887096  0.8984417
## test_prepnone:wkly_study_hours10-May                    1.3751968  0.7327249
## parent_marital_statusmarried:wkly_study_hours> 10       0.5059311  1.2701017
## parent_marital_statussingle:wkly_study_hours> 10        1.5241711  1.4383179
## parent_marital_statuswidowed:wkly_study_hours> 10       0.4014271  3.6908441
## parent_marital_statusmarried:wkly_study_hours10-May     3.0172746  0.9604939
## parent_marital_statussingle:wkly_study_hours10-May      3.9778930  1.0695335
## parent_marital_statuswidowed:wkly_study_hours10-May     4.4176050  3.1514433
## practice_sportregularly:is_first_childyes              -2.1435734  1.0927088
## practice_sportsometimes:is_first_childyes              -1.6813218  1.0702264
## transport_meansschool_bus:reading_score                 0.0403894  0.0199814
## math_score:reading_score                               -0.0019615  0.0004987
##                                                        t value Pr(>|t|)    
## (Intercept)                                              2.137 0.033072 *  
## gendermale                                              -3.800 0.000163 ***
## ethnic_groupgroup B                                     -2.553 0.010983 *  
## ethnic_groupgroup C                                     -1.884 0.060142 .  
## ethnic_groupgroup D                                     -0.790 0.429895    
## ethnic_groupgroup E                                     -1.417 0.157209    
## parent_educbachelor's degree                            -0.942 0.346717    
## parent_educhigh school                                  -0.655 0.512998    
## parent_educmaster's degree                               1.695 0.090720 .  
## parent_educsome college                                 -1.195 0.232690    
## parent_educsome high school                             -0.568 0.570286    
## lunch_typestandard                                       0.427 0.669439    
## test_prepnone                                           -3.361 0.000835 ***
## parent_marital_statusmarried                            -1.787 0.074575 .  
## parent_marital_statussingle                             -1.197 0.231850    
## parent_marital_statuswidowed                            -0.405 0.685897    
## practice_sportregularly                                  2.050 0.040902 *  
## practice_sportsometimes                                  1.622 0.105493    
## is_first_childyes                                       -1.265 0.206531    
## transport_meansschool_bus                               -1.922 0.055127 .  
## wkly_study_hours> 10                                    -1.156 0.248390    
## wkly_study_hours10-May                                  -3.563 0.000402 ***
## math_score                                               6.399 3.63e-10 ***
## reading_score                                           12.124  < 2e-16 ***
## gendermale:ethnic_groupgroup B                          -1.699 0.089938 .  
## gendermale:ethnic_groupgroup C                          -1.728 0.084524 .  
## gendermale:ethnic_groupgroup D                          -0.627 0.531215    
## gendermale:ethnic_groupgroup E                          -1.875 0.061422 .  
## gendermale:math_score                                   -1.415 0.157681    
## gendermale:reading_score                                 1.813 0.070402 .  
## ethnic_groupgroup B:test_prepnone                        1.019 0.308670    
## ethnic_groupgroup C:test_prepnone                       -0.157 0.875620    
## ethnic_groupgroup D:test_prepnone                       -0.956 0.339540    
## ethnic_groupgroup E:test_prepnone                        0.284 0.776850    
## ethnic_groupgroup B:is_first_childyes                    1.700 0.089722 .  
## ethnic_groupgroup C:is_first_childyes                    2.720 0.006752 ** 
## ethnic_groupgroup D:is_first_childyes                    1.764 0.078395 .  
## ethnic_groupgroup E:is_first_childyes                    2.047 0.041215 *  
## ethnic_groupgroup B:math_score                           2.591 0.009863 ** 
## ethnic_groupgroup C:math_score                           2.177 0.029978 *  
## ethnic_groupgroup D:math_score                           1.698 0.090225 .  
## ethnic_groupgroup E:math_score                           1.377 0.169166    
## parent_educbachelor's degree:lunch_typestandard         -0.575 0.565322    
## parent_educhigh school:lunch_typestandard                1.009 0.313571    
## parent_educmaster's degree:lunch_typestandard           -0.322 0.747292    
## parent_educsome college:lunch_typestandard               2.519 0.012074 *  
## parent_educsome high school:lunch_typestandard           0.605 0.545357    
## parent_educbachelor's degree:practice_sportregularly     1.260 0.208421    
## parent_educhigh school:practice_sportregularly           1.250 0.211737    
## parent_educmaster's degree:practice_sportregularly      -0.249 0.803300    
## parent_educsome college:practice_sportregularly          0.301 0.763756    
## parent_educsome high school:practice_sportregularly     -0.709 0.478480    
## parent_educbachelor's degree:practice_sportsometimes     0.371 0.710472    
## parent_educhigh school:practice_sportsometimes           0.823 0.410694    
## parent_educmaster's degree:practice_sportsometimes      -1.407 0.159915    
## parent_educsome college:practice_sportsometimes          1.290 0.197774    
## parent_educsome high school:practice_sportsometimes     -2.106 0.035732 *  
## parent_educbachelor's degree:is_first_childyes           2.481 0.013443 *  
## parent_educhigh school:is_first_childyes                 2.112 0.035201 *  
## parent_educmaster's degree:is_first_childyes            -1.723 0.085579 .  
## parent_educsome college:is_first_childyes                3.059 0.002339 ** 
## parent_educsome high school:is_first_childyes            2.304 0.021653 *  
## parent_educbachelor's degree:transport_meansschool_bus   0.213 0.831211    
## parent_educhigh school:transport_meansschool_bus         1.218 0.223937    
## parent_educmaster's degree:transport_meansschool_bus    -0.716 0.474091    
## parent_educsome college:transport_meansschool_bus       -1.153 0.249343    
## parent_educsome high school:transport_meansschool_bus    1.777 0.076107 .  
## parent_educbachelor's degree:math_score                 -1.341 0.180651    
## parent_educhigh school:math_score                       -1.325 0.185817    
## parent_educmaster's degree:math_score                    1.696 0.090538 .  
## parent_educsome college:math_score                      -1.102 0.271054    
## parent_educsome high school:math_score                  -2.271 0.023572 *  
## parent_educbachelor's degree:reading_score               1.535 0.125539    
## parent_educhigh school:reading_score                     0.228 0.819907    
## parent_educmaster's degree:reading_score                -1.380 0.168067    
## parent_educsome college:reading_score                    0.868 0.386059    
## parent_educsome high school:reading_score                1.820 0.069330 .  
## lunch_typestandard:parent_marital_statusmarried         -0.078 0.937985    
## lunch_typestandard:parent_marital_statussingle          -1.692 0.091286 .  
## lunch_typestandard:parent_marital_statuswidowed         -0.797 0.425633    
## lunch_typestandard:is_first_childyes                    -1.303 0.193216    
## test_prepnone:wkly_study_hours> 10                       0.989 0.323062    
## test_prepnone:wkly_study_hours10-May                     1.877 0.061128 .  
## parent_marital_statusmarried:wkly_study_hours> 10        0.398 0.690551    
## parent_marital_statussingle:wkly_study_hours> 10         1.060 0.289800    
## parent_marital_statuswidowed:wkly_study_hours> 10        0.109 0.913434    
## parent_marital_statusmarried:wkly_study_hours10-May      3.141 0.001782 ** 
## parent_marital_statussingle:wkly_study_hours10-May       3.719 0.000223 ***
## parent_marital_statuswidowed:wkly_study_hours10-May      1.402 0.161608    
## practice_sportregularly:is_first_childyes               -1.962 0.050354 .  
## practice_sportsometimes:is_first_childyes               -1.571 0.116820    
## transport_meansschool_bus:reading_score                  2.021 0.043779 *  
## math_score:reading_score                                -3.933 9.58e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.174 on 497 degrees of freedom
## Multiple R-squared:  0.9648, Adjusted R-squared:  0.9582 
## F-statistic: 147.9 on 92 and 497 DF,  p-value: < 2.2e-16

MAth Score

df_4_mdl_math2=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,math_score,writing_score,reading_score)
full_fit_math2=lm(math_score ~ .^2,data=df_4_mdl_math2)
summary(full_fit_math2)
## 
## Call:
## lm(formula = math_score ~ .^2, data = df_4_mdl_math2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.8339  -2.5556   0.0729   2.6772  13.5028 
## 
## Coefficients: (6 not defined because of singularities)
##                                                             Estimate Std. Error
## (Intercept)                                               -10.063553  15.902031
## gendermale                                                 19.979949   5.459084
## ethnic_groupgroup B                                        -9.908045  10.348115
## ethnic_groupgroup C                                        -2.674303   9.698450
## ethnic_groupgroup D                                        -9.291267  10.188392
## ethnic_groupgroup E                                        -1.524115  10.431088
## parent_educbachelor's degree                                5.105902   9.603385
## parent_educhigh school                                     11.274516   7.461425
## parent_educmaster's degree                                  7.611157  12.261135
## parent_educsome college                                    12.078740   7.028940
## parent_educsome high school                                 9.863557   7.124145
## lunch_typestandard                                          0.183473   5.580042
## test_prepnone                                               3.845622   5.998419
## parent_marital_statusmarried                               -5.351981   7.427840
## parent_marital_statussingle                                -5.776894   8.655300
## parent_marital_statuswidowed                               29.751199  18.491697
## practice_sportregularly                                    -3.461686   9.557641
## practice_sportsometimes                                     0.109714   9.474618
## is_first_childyes                                          -5.079237   5.489364
## transport_meansschool_bus                                   9.835872   5.235990
## wkly_study_hours> 10                                       -0.198662   7.886884
## wkly_study_hours10-May                                     -4.915573   6.280515
## writing_score                                               0.684852   0.559961
## reading_score                                               0.240577   0.527297
## gendermale:ethnic_groupgroup B                              0.726299   2.951228
## gendermale:ethnic_groupgroup C                              2.276796   2.787315
## gendermale:ethnic_groupgroup D                             -0.233296   2.850301
## gendermale:ethnic_groupgroup E                              2.280813   3.128047
## gendermale:parent_educbachelor's degree                    -2.133728   2.269909
## gendermale:parent_educhigh school                          -0.882648   1.878208
## gendermale:parent_educmaster's degree                       1.952760   2.985466
## gendermale:parent_educsome college                         -0.726275   2.039503
## gendermale:parent_educsome high school                     -0.361364   1.999148
## gendermale:lunch_typestandard                              -0.523858   1.442766
## gendermale:test_prepnone                                   -0.723812   1.451024
## gendermale:parent_marital_statusmarried                    -0.307346   1.916842
## gendermale:parent_marital_statussingle                      0.060258   2.142298
## gendermale:parent_marital_statuswidowed                    -2.429801   8.143220
## gendermale:practice_sportregularly                         -0.219895   2.295823
## gendermale:practice_sportsometimes                          0.137348   2.237267
## gendermale:is_first_childyes                               -0.086440   1.378812
## gendermale:transport_meansschool_bus                       -0.956230   1.365940
## gendermale:wkly_study_hours> 10                             0.398251   1.960905
## gendermale:wkly_study_hours10-May                          -0.385080   1.534527
## gendermale:writing_score                                   -0.141074   0.162549
## gendermale:reading_score                                    0.075694   0.159839
## ethnic_groupgroup B:parent_educbachelor's degree            0.266536   6.073313
## ethnic_groupgroup C:parent_educbachelor's degree           -0.409047   6.020229
## ethnic_groupgroup D:parent_educbachelor's degree            5.112680   5.922853
## ethnic_groupgroup E:parent_educbachelor's degree            3.128234   6.753621
## ethnic_groupgroup B:parent_educhigh school                  4.280505   3.674482
## ethnic_groupgroup C:parent_educhigh school                  3.348883   3.501663
## ethnic_groupgroup D:parent_educhigh school                  4.483079   3.582679
## ethnic_groupgroup E:parent_educhigh school                  4.840534   3.987015
## ethnic_groupgroup B:parent_educmaster's degree             -5.305727   8.241169
## ethnic_groupgroup C:parent_educmaster's degree             -4.417568   7.468955
## ethnic_groupgroup D:parent_educmaster's degree             -3.655068   7.623938
## ethnic_groupgroup E:parent_educmaster's degree             -7.258787   7.987115
## ethnic_groupgroup B:parent_educsome college                 1.180947   4.107385
## ethnic_groupgroup C:parent_educsome college                -2.520179   3.822148
## ethnic_groupgroup D:parent_educsome college                 4.656424   4.059229
## ethnic_groupgroup E:parent_educsome college                 0.868305   4.119982
## ethnic_groupgroup B:parent_educsome high school             3.931608   3.971208
## ethnic_groupgroup C:parent_educsome high school             5.763745   3.640055
## ethnic_groupgroup D:parent_educsome high school             6.721231   3.619185
## ethnic_groupgroup E:parent_educsome high school             8.083832   3.997528
## ethnic_groupgroup B:lunch_typestandard                      0.649125   2.845967
## ethnic_groupgroup C:lunch_typestandard                      0.149832   2.781119
## ethnic_groupgroup D:lunch_typestandard                      0.013271   2.852599
## ethnic_groupgroup E:lunch_typestandard                      1.126956   3.135033
## ethnic_groupgroup B:test_prepnone                           1.194401   3.148845
## ethnic_groupgroup C:test_prepnone                           2.898886   3.013236
## ethnic_groupgroup D:test_prepnone                           3.927748   3.059021
## ethnic_groupgroup E:test_prepnone                           2.355490   3.166365
## ethnic_groupgroup B:parent_marital_statusmarried           -0.496261   3.994810
## ethnic_groupgroup C:parent_marital_statusmarried            1.607295   3.607491
## ethnic_groupgroup D:parent_marital_statusmarried            0.160941   3.624540
## ethnic_groupgroup E:parent_marital_statusmarried            1.840181   3.909171
## ethnic_groupgroup B:parent_marital_statussingle            -1.465260   4.720518
## ethnic_groupgroup C:parent_marital_statussingle            -1.662000   4.440701
## ethnic_groupgroup D:parent_marital_statussingle            -2.754752   4.374864
## ethnic_groupgroup E:parent_marital_statussingle             0.221434   4.910902
## ethnic_groupgroup B:parent_marital_statuswidowed           53.999583  46.909620
## ethnic_groupgroup C:parent_marital_statuswidowed           43.335261  39.315988
## ethnic_groupgroup D:parent_marital_statuswidowed           24.204499  37.893825
## ethnic_groupgroup E:parent_marital_statuswidowed                  NA         NA
## ethnic_groupgroup B:practice_sportregularly                 2.178723   4.822899
## ethnic_groupgroup C:practice_sportregularly                -2.765314   4.824426
## ethnic_groupgroup D:practice_sportregularly                 0.522775   5.327167
## ethnic_groupgroup E:practice_sportregularly                 1.889530   4.895585
## ethnic_groupgroup B:practice_sportsometimes                -1.027920   5.181840
## ethnic_groupgroup C:practice_sportsometimes                -4.658836   5.029009
## ethnic_groupgroup D:practice_sportsometimes                -2.547327   5.540338
## ethnic_groupgroup E:practice_sportsometimes                -2.423983   5.074061
## ethnic_groupgroup B:is_first_childyes                       2.253002   2.795124
## ethnic_groupgroup C:is_first_childyes                      -1.900435   2.623197
## ethnic_groupgroup D:is_first_childyes                       0.801293   2.692236
## ethnic_groupgroup E:is_first_childyes                       1.905110   2.995054
## ethnic_groupgroup B:transport_meansschool_bus               1.299631   2.764491
## ethnic_groupgroup C:transport_meansschool_bus              -0.382605   2.516104
## ethnic_groupgroup D:transport_meansschool_bus               1.299017   2.578520
## ethnic_groupgroup E:transport_meansschool_bus              -0.438980   2.964843
## ethnic_groupgroup B:wkly_study_hours> 10                   -1.612323   4.522319
## ethnic_groupgroup C:wkly_study_hours> 10                    0.750639   4.460950
## ethnic_groupgroup D:wkly_study_hours> 10                   -0.030054   4.584488
## ethnic_groupgroup E:wkly_study_hours> 10                   -3.704460   4.783248
## ethnic_groupgroup B:wkly_study_hours10-May                  0.880976   3.750203
## ethnic_groupgroup C:wkly_study_hours10-May                  1.603776   3.678274
## ethnic_groupgroup D:wkly_study_hours10-May                  2.294593   3.788306
## ethnic_groupgroup E:wkly_study_hours10-May                 -0.205759   3.997181
## ethnic_groupgroup B:writing_score                           0.345499   0.385190
## ethnic_groupgroup C:writing_score                           0.772633   0.385880
## ethnic_groupgroup D:writing_score                           0.329808   0.369938
## ethnic_groupgroup E:writing_score                           0.391206   0.423163
## ethnic_groupgroup B:reading_score                          -0.273203   0.350590
## ethnic_groupgroup C:reading_score                          -0.736787   0.346373
## ethnic_groupgroup D:reading_score                          -0.300445   0.328527
## ethnic_groupgroup E:reading_score                          -0.392592   0.379670
## parent_educbachelor's degree:lunch_typestandard             2.806697   2.334257
## parent_educhigh school:lunch_typestandard                   0.351138   1.917046
## parent_educmaster's degree:lunch_typestandard               7.747509   3.797623
## parent_educsome college:lunch_typestandard                 -1.011932   1.954360
## parent_educsome high school:lunch_typestandard              2.357029   2.032294
## parent_educbachelor's degree:test_prepnone                 -3.744743   2.262348
## parent_educhigh school:test_prepnone                       -4.623184   2.230928
## parent_educmaster's degree:test_prepnone                   -1.544119   3.901916
## parent_educsome college:test_prepnone                      -2.136444   2.034417
## parent_educsome high school:test_prepnone                  -0.252416   2.014710
## parent_educbachelor's degree:parent_marital_statusmarried  -0.242286   3.989639
## parent_educhigh school:parent_marital_statusmarried         0.147874   2.715992
## parent_educmaster's degree:parent_marital_statusmarried    -0.990220   3.975562
## parent_educsome college:parent_marital_statusmarried       -2.845243   2.585056
## parent_educsome high school:parent_marital_statusmarried   -3.677034   2.555259
## parent_educbachelor's degree:parent_marital_statussingle   -3.105257   4.433246
## parent_educhigh school:parent_marital_statussingle         -2.274837   2.908985
## parent_educmaster's degree:parent_marital_statussingle     -2.966605   4.070481
## parent_educsome college:parent_marital_statussingle        -4.249023   2.847743
## parent_educsome high school:parent_marital_statussingle    -7.265951   2.885139
## parent_educbachelor's degree:parent_marital_statuswidowed -25.157857  38.391984
## parent_educhigh school:parent_marital_statuswidowed       -56.697558  42.960058
## parent_educmaster's degree:parent_marital_statuswidowed   -18.315841  23.322283
## parent_educsome college:parent_marital_statuswidowed      -44.785634  29.087158
## parent_educsome high school:parent_marital_statuswidowed  -49.558775  34.314653
## parent_educbachelor's degree:practice_sportregularly       -1.878258   4.113427
## parent_educhigh school:practice_sportregularly             -3.026737   3.403576
## parent_educmaster's degree:practice_sportregularly         -2.889508   4.825030
## parent_educsome college:practice_sportregularly            -0.934756   3.322442
## parent_educsome high school:practice_sportregularly        -0.508045   3.143744
## parent_educbachelor's degree:practice_sportsometimes       -0.928893   3.843274
## parent_educhigh school:practice_sportsometimes             -2.820167   3.170622
## parent_educmaster's degree:practice_sportsometimes          1.517356   4.320902
## parent_educsome college:practice_sportsometimes            -1.707788   3.263860
## parent_educsome high school:practice_sportsometimes         1.501770   3.009011
## parent_educbachelor's degree:is_first_childyes             -4.568113   2.240752
## parent_educhigh school:is_first_childyes                    0.296732   1.979188
## parent_educmaster's degree:is_first_childyes               -0.359355   3.556613
## parent_educsome college:is_first_childyes                  -2.848291   1.954179
## parent_educsome high school:is_first_childyes              -3.015449   2.009189
## parent_educbachelor's degree:transport_meansschool_bus      3.417597   2.251578
## parent_educhigh school:transport_meansschool_bus           -0.892789   1.859944
## parent_educmaster's degree:transport_meansschool_bus        5.137701   2.843312
## parent_educsome college:transport_meansschool_bus           1.077925   1.838100
## parent_educsome high school:transport_meansschool_bus      -0.425194   1.983677
## parent_educbachelor's degree:wkly_study_hours> 10          -4.895661   3.340936
## parent_educhigh school:wkly_study_hours> 10                -0.988402   2.793862
## parent_educmaster's degree:wkly_study_hours> 10            13.852329   6.344763
## parent_educsome college:wkly_study_hours> 10                0.440856   2.846617
## parent_educsome high school:wkly_study_hours> 10           -2.255143   2.982901
## parent_educbachelor's degree:wkly_study_hours10-May        -0.318695   2.380671
## parent_educhigh school:wkly_study_hours10-May               1.516532   2.213374
## parent_educmaster's degree:wkly_study_hours10-May           5.362770   3.326750
## parent_educsome college:wkly_study_hours10-May              2.359546   2.271351
## parent_educsome high school:wkly_study_hours10-May         -0.671573   2.402536
## parent_educbachelor's degree:writing_score                 -0.575083   0.309893
## parent_educhigh school:writing_score                       -0.241471   0.236755
## parent_educmaster's degree:writing_score                   -0.987477   0.401391
## parent_educsome college:writing_score                      -0.111567   0.232350
## parent_educsome high school:writing_score                  -0.252211   0.239952
## parent_educbachelor's degree:reading_score                  0.532131   0.305768
## parent_educhigh school:reading_score                        0.127341   0.223323
## parent_educmaster's degree:reading_score                    0.781120   0.379454
## parent_educsome college:reading_score                       0.018921   0.226178
## parent_educsome high school:reading_score                   0.129713   0.227434
## lunch_typestandard:test_prepnone                            0.967232   1.564850
## lunch_typestandard:parent_marital_statusmarried             0.413586   1.899033
## lunch_typestandard:parent_marital_statussingle              1.216538   2.240827
## lunch_typestandard:parent_marital_statuswidowed           -40.531993  34.813124
## lunch_typestandard:practice_sportregularly                  3.093980   2.411249
## lunch_typestandard:practice_sportsometimes                  0.889797   2.273015
## lunch_typestandard:is_first_childyes                        3.167617   1.531708
## lunch_typestandard:transport_meansschool_bus                0.906158   1.368022
## lunch_typestandard:wkly_study_hours> 10                    -1.037156   2.138762
## lunch_typestandard:wkly_study_hours10-May                   0.591177   1.575608
## lunch_typestandard:writing_score                            0.034891   0.167930
## lunch_typestandard:reading_score                           -0.083186   0.160327
## test_prepnone:parent_marital_statusmarried                  3.711770   1.981008
## test_prepnone:parent_marital_statussingle                   4.203078   2.274322
## test_prepnone:parent_marital_statuswidowed                -25.734438  19.037555
## test_prepnone:practice_sportregularly                       0.622014   2.608208
## test_prepnone:practice_sportsometimes                      -0.090258   2.532121
## test_prepnone:is_first_childyes                            -0.100121   1.452427
## test_prepnone:transport_meansschool_bus                    -3.781701   1.377571
## test_prepnone:wkly_study_hours> 10                         -1.704914   2.181380
## test_prepnone:wkly_study_hours10-May                       -0.499473   1.707231
## test_prepnone:writing_score                                -0.002329   0.160709
## test_prepnone:reading_score                                -0.017549   0.153865
## parent_marital_statusmarried:practice_sportregularly        3.691614   2.969841
## parent_marital_statussingle:practice_sportregularly         8.454559   4.002755
## parent_marital_statuswidowed:practice_sportregularly       35.814726  36.605884
## parent_marital_statusmarried:practice_sportsometimes        3.394713   2.916995
## parent_marital_statussingle:practice_sportsometimes         6.154316   3.923684
## parent_marital_statuswidowed:practice_sportsometimes              NA         NA
## parent_marital_statusmarried:is_first_childyes              2.721610   2.325975
## parent_marital_statussingle:is_first_childyes               2.965264   2.518058
## parent_marital_statuswidowed:is_first_childyes             15.630050  13.811686
## parent_marital_statusmarried:transport_meansschool_bus      0.998178   1.877298
## parent_marital_statussingle:transport_meansschool_bus      -1.394931   2.108507
## parent_marital_statuswidowed:transport_meansschool_bus    -15.572097   8.889319
## parent_marital_statusmarried:wkly_study_hours> 10          -2.240703   3.119485
## parent_marital_statussingle:wkly_study_hours> 10           -4.190052   3.377709
## parent_marital_statuswidowed:wkly_study_hours> 10                 NA         NA
## parent_marital_statusmarried:wkly_study_hours10-May        -2.935616   2.048140
## parent_marital_statussingle:wkly_study_hours10-May         -2.480476   2.292557
## parent_marital_statuswidowed:wkly_study_hours10-May               NA         NA
## parent_marital_statusmarried:writing_score                  0.088260   0.236092
## parent_marital_statussingle:writing_score                  -0.071441   0.261043
## parent_marital_statuswidowed:writing_score                        NA         NA
## parent_marital_statusmarried:reading_score                 -0.076255   0.237211
## parent_marital_statussingle:reading_score                   0.097786   0.261926
## parent_marital_statuswidowed:reading_score                        NA         NA
## practice_sportregularly:is_first_childyes                   3.073565   2.674564
## practice_sportsometimes:is_first_childyes                   2.274435   2.611838
## practice_sportregularly:transport_meansschool_bus           0.457526   2.281489
## practice_sportsometimes:transport_meansschool_bus          -0.873418   2.183510
## practice_sportregularly:wkly_study_hours> 10               -2.679282   3.113849
## practice_sportsometimes:wkly_study_hours> 10               -2.365542   3.078446
## practice_sportregularly:wkly_study_hours10-May              0.248807   2.505147
## practice_sportsometimes:wkly_study_hours10-May              1.249728   2.457903
## practice_sportregularly:writing_score                       0.131987   0.299697
## practice_sportsometimes:writing_score                       0.262157   0.288717
## practice_sportregularly:reading_score                      -0.176254   0.279436
## practice_sportsometimes:reading_score                      -0.286414   0.260580
## is_first_childyes:transport_meansschool_bus                -2.449507   1.350503
## is_first_childyes:wkly_study_hours> 10                      0.017162   1.996805
## is_first_childyes:wkly_study_hours10-May                   -2.853518   1.502404
## is_first_childyes:writing_score                            -0.053821   0.167561
## is_first_childyes:reading_score                             0.095788   0.162449
## transport_meansschool_bus:wkly_study_hours> 10              2.207347   1.944391
## transport_meansschool_bus:wkly_study_hours10-May            1.057296   1.386729
## transport_meansschool_bus:writing_score                    -0.105436   0.166591
## transport_meansschool_bus:reading_score                    -0.012356   0.160606
## wkly_study_hours> 10:writing_score                         -0.330908   0.243684
## wkly_study_hours10-May:writing_score                       -0.323872   0.179972
## wkly_study_hours> 10:reading_score                          0.450819   0.237669
## wkly_study_hours10-May:reading_score                        0.413381   0.173792
## writing_score:reading_score                                 0.001094   0.001427
##                                                           t value Pr(>|t|)    
## (Intercept)                                                -0.633 0.527259    
## gendermale                                                  3.660 0.000292 ***
## ethnic_groupgroup B                                        -0.957 0.339009    
## ethnic_groupgroup C                                        -0.276 0.782911    
## ethnic_groupgroup D                                        -0.912 0.362443    
## ethnic_groupgroup E                                        -0.146 0.883919    
## parent_educbachelor's degree                                0.532 0.595297    
## parent_educhigh school                                      1.511 0.131707    
## parent_educmaster's degree                                  0.621 0.535177    
## parent_educsome college                                     1.718 0.086629 .  
## parent_educsome high school                                 1.385 0.167106    
## lunch_typestandard                                          0.033 0.973789    
## test_prepnone                                               0.641 0.521886    
## parent_marital_statusmarried                               -0.721 0.471694    
## parent_marital_statussingle                                -0.667 0.504944    
## parent_marital_statuswidowed                                1.609 0.108567    
## practice_sportregularly                                    -0.362 0.717435    
## practice_sportsometimes                                     0.012 0.990768    
## is_first_childyes                                          -0.925 0.355473    
## transport_meansschool_bus                                   1.879 0.061167 .  
## wkly_study_hours> 10                                       -0.025 0.979919    
## wkly_study_hours10-May                                     -0.783 0.434366    
## writing_score                                               1.223 0.222163    
## reading_score                                               0.456 0.648505    
## gendermale:ethnic_groupgroup B                              0.246 0.805753    
## gendermale:ethnic_groupgroup C                              0.817 0.414591    
## gendermale:ethnic_groupgroup D                             -0.082 0.934815    
## gendermale:ethnic_groupgroup E                              0.729 0.466412    
## gendermale:parent_educbachelor's degree                    -0.940 0.347882    
## gendermale:parent_educhigh school                          -0.470 0.638698    
## gendermale:parent_educmaster's degree                       0.654 0.513497    
## gendermale:parent_educsome college                         -0.356 0.721983    
## gendermale:parent_educsome high school                     -0.181 0.856665    
## gendermale:lunch_typestandard                              -0.363 0.716761    
## gendermale:test_prepnone                                   -0.499 0.618223    
## gendermale:parent_marital_statusmarried                    -0.160 0.872709    
## gendermale:parent_marital_statussingle                      0.028 0.977577    
## gendermale:parent_marital_statuswidowed                    -0.298 0.765593    
## gendermale:practice_sportregularly                         -0.096 0.923751    
## gendermale:practice_sportsometimes                          0.061 0.951084    
## gendermale:is_first_childyes                               -0.063 0.950049    
## gendermale:transport_meansschool_bus                       -0.700 0.484373    
## gendermale:wkly_study_hours> 10                             0.203 0.839182    
## gendermale:wkly_study_hours10-May                          -0.251 0.802009    
## gendermale:writing_score                                   -0.868 0.386070    
## gendermale:reading_score                                    0.474 0.636113    
## ethnic_groupgroup B:parent_educbachelor's degree            0.044 0.965021    
## ethnic_groupgroup C:parent_educbachelor's degree           -0.068 0.945869    
## ethnic_groupgroup D:parent_educbachelor's degree            0.863 0.388629    
## ethnic_groupgroup E:parent_educbachelor's degree            0.463 0.643522    
## ethnic_groupgroup B:parent_educhigh school                  1.165 0.244865    
## ethnic_groupgroup C:parent_educhigh school                  0.956 0.339565    
## ethnic_groupgroup D:parent_educhigh school                  1.251 0.211678    
## ethnic_groupgroup E:parent_educhigh school                  1.214 0.225562    
## ethnic_groupgroup B:parent_educmaster's degree             -0.644 0.520134    
## ethnic_groupgroup C:parent_educmaster's degree             -0.591 0.554607    
## ethnic_groupgroup D:parent_educmaster's degree             -0.479 0.631948    
## ethnic_groupgroup E:parent_educmaster's degree             -0.909 0.364093    
## ethnic_groupgroup B:parent_educsome college                 0.288 0.773891    
## ethnic_groupgroup C:parent_educsome college                -0.659 0.510110    
## ethnic_groupgroup D:parent_educsome college                 1.147 0.252138    
## ethnic_groupgroup E:parent_educsome college                 0.211 0.833205    
## ethnic_groupgroup B:parent_educsome high school             0.990 0.322864    
## ethnic_groupgroup C:parent_educsome high school             1.583 0.114255    
## ethnic_groupgroup D:parent_educsome high school             1.857 0.064160 .  
## ethnic_groupgroup E:parent_educsome high school             2.022 0.043938 *  
## ethnic_groupgroup B:lunch_typestandard                      0.228 0.819717    
## ethnic_groupgroup C:lunch_typestandard                      0.054 0.957067    
## ethnic_groupgroup D:lunch_typestandard                      0.005 0.996291    
## ethnic_groupgroup E:lunch_typestandard                      0.359 0.719465    
## ethnic_groupgroup B:test_prepnone                           0.379 0.704691    
## ethnic_groupgroup C:test_prepnone                           0.962 0.336708    
## ethnic_groupgroup D:test_prepnone                           1.284 0.200020    
## ethnic_groupgroup E:test_prepnone                           0.744 0.457445    
## ethnic_groupgroup B:parent_marital_statusmarried           -0.124 0.901209    
## ethnic_groupgroup C:parent_marital_statusmarried            0.446 0.656210    
## ethnic_groupgroup D:parent_marital_statusmarried            0.044 0.964609    
## ethnic_groupgroup E:parent_marital_statusmarried            0.471 0.638132    
## ethnic_groupgroup B:parent_marital_statussingle            -0.310 0.756445    
## ethnic_groupgroup C:parent_marital_statussingle            -0.374 0.708440    
## ethnic_groupgroup D:parent_marital_statussingle            -0.630 0.529329    
## ethnic_groupgroup E:parent_marital_statussingle             0.045 0.964062    
## ethnic_groupgroup B:parent_marital_statuswidowed            1.151 0.250483    
## ethnic_groupgroup C:parent_marital_statuswidowed            1.102 0.271141    
## ethnic_groupgroup D:parent_marital_statuswidowed            0.639 0.523419    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                 0.452 0.651740    
## ethnic_groupgroup C:practice_sportregularly                -0.573 0.566895    
## ethnic_groupgroup D:practice_sportregularly                 0.098 0.921884    
## ethnic_groupgroup E:practice_sportregularly                 0.386 0.699763    
## ethnic_groupgroup B:practice_sportsometimes                -0.198 0.842874    
## ethnic_groupgroup C:practice_sportsometimes                -0.926 0.354899    
## ethnic_groupgroup D:practice_sportsometimes                -0.460 0.645969    
## ethnic_groupgroup E:practice_sportsometimes                -0.478 0.633156    
## ethnic_groupgroup B:is_first_childyes                       0.806 0.420779    
## ethnic_groupgroup C:is_first_childyes                      -0.724 0.469274    
## ethnic_groupgroup D:is_first_childyes                       0.298 0.766166    
## ethnic_groupgroup E:is_first_childyes                       0.636 0.525149    
## ethnic_groupgroup B:transport_meansschool_bus               0.470 0.638574    
## ethnic_groupgroup C:transport_meansschool_bus              -0.152 0.879228    
## ethnic_groupgroup D:transport_meansschool_bus               0.504 0.614740    
## ethnic_groupgroup E:transport_meansschool_bus              -0.148 0.882382    
## ethnic_groupgroup B:wkly_study_hours> 10                   -0.357 0.721668    
## ethnic_groupgroup C:wkly_study_hours> 10                    0.168 0.866472    
## ethnic_groupgroup D:wkly_study_hours> 10                   -0.007 0.994773    
## ethnic_groupgroup E:wkly_study_hours> 10                   -0.774 0.439194    
## ethnic_groupgroup B:wkly_study_hours10-May                  0.235 0.814417    
## ethnic_groupgroup C:wkly_study_hours10-May                  0.436 0.663104    
## ethnic_groupgroup D:wkly_study_hours10-May                  0.606 0.545115    
## ethnic_groupgroup E:wkly_study_hours10-May                 -0.051 0.958976    
## ethnic_groupgroup B:writing_score                           0.897 0.370377    
## ethnic_groupgroup C:writing_score                           2.002 0.046050 *  
## ethnic_groupgroup D:writing_score                           0.892 0.373280    
## ethnic_groupgroup E:writing_score                           0.924 0.355891    
## ethnic_groupgroup B:reading_score                          -0.779 0.436365    
## ethnic_groupgroup C:reading_score                          -2.127 0.034127 *  
## ethnic_groupgroup D:reading_score                          -0.915 0.361091    
## ethnic_groupgroup E:reading_score                          -1.034 0.301855    
## parent_educbachelor's degree:lunch_typestandard             1.202 0.230048    
## parent_educhigh school:lunch_typestandard                   0.183 0.854777    
## parent_educmaster's degree:lunch_typestandard               2.040 0.042113 *  
## parent_educsome college:lunch_typestandard                 -0.518 0.604947    
## parent_educsome high school:lunch_typestandard              1.160 0.246949    
## parent_educbachelor's degree:test_prepnone                 -1.655 0.098797 .  
## parent_educhigh school:test_prepnone                       -2.072 0.038989 *  
## parent_educmaster's degree:test_prepnone                   -0.396 0.692550    
## parent_educsome college:test_prepnone                      -1.050 0.294395    
## parent_educsome high school:test_prepnone                  -0.125 0.900371    
## parent_educbachelor's degree:parent_marital_statusmarried  -0.061 0.951611    
## parent_educhigh school:parent_marital_statusmarried         0.054 0.956612    
## parent_educmaster's degree:parent_marital_statusmarried    -0.249 0.803452    
## parent_educsome college:parent_marital_statusmarried       -1.101 0.271827    
## parent_educsome high school:parent_marital_statusmarried   -1.439 0.151069    
## parent_educbachelor's degree:parent_marital_statussingle   -0.700 0.484127    
## parent_educhigh school:parent_marital_statussingle         -0.782 0.434757    
## parent_educmaster's degree:parent_marital_statussingle     -0.729 0.466620    
## parent_educsome college:parent_marital_statussingle        -1.492 0.136609    
## parent_educsome high school:parent_marital_statussingle    -2.518 0.012247 *  
## parent_educbachelor's degree:parent_marital_statuswidowed  -0.655 0.512725    
## parent_educhigh school:parent_marital_statuswidowed        -1.320 0.187798    
## parent_educmaster's degree:parent_marital_statuswidowed    -0.785 0.432803    
## parent_educsome college:parent_marital_statuswidowed       -1.540 0.124562    
## parent_educsome high school:parent_marital_statuswidowed   -1.444 0.149591    
## parent_educbachelor's degree:practice_sportregularly       -0.457 0.648238    
## parent_educhigh school:practice_sportregularly             -0.889 0.374481    
## parent_educmaster's degree:practice_sportregularly         -0.599 0.549666    
## parent_educsome college:practice_sportregularly            -0.281 0.778616    
## parent_educsome high school:practice_sportregularly        -0.162 0.871713    
## parent_educbachelor's degree:practice_sportsometimes       -0.242 0.809164    
## parent_educhigh school:practice_sportsometimes             -0.889 0.374381    
## parent_educmaster's degree:practice_sportsometimes          0.351 0.725681    
## parent_educsome college:practice_sportsometimes            -0.523 0.601147    
## parent_educsome high school:practice_sportsometimes         0.499 0.618038    
## parent_educbachelor's degree:is_first_childyes             -2.039 0.042258 *  
## parent_educhigh school:is_first_childyes                    0.150 0.880912    
## parent_educmaster's degree:is_first_childyes               -0.101 0.919579    
## parent_educsome college:is_first_childyes                  -1.458 0.145891    
## parent_educsome high school:is_first_childyes              -1.501 0.134328    
## parent_educbachelor's degree:transport_meansschool_bus      1.518 0.129977    
## parent_educhigh school:transport_meansschool_bus           -0.480 0.631530    
## parent_educmaster's degree:transport_meansschool_bus        1.807 0.071655 .  
## parent_educsome college:transport_meansschool_bus           0.586 0.557973    
## parent_educsome high school:transport_meansschool_bus      -0.214 0.830406    
## parent_educbachelor's degree:wkly_study_hours> 10          -1.465 0.143748    
## parent_educhigh school:wkly_study_hours> 10                -0.354 0.723726    
## parent_educmaster's degree:wkly_study_hours> 10             2.183 0.029699 *  
## parent_educsome college:wkly_study_hours> 10                0.155 0.877016    
## parent_educsome high school:wkly_study_hours> 10           -0.756 0.450159    
## parent_educbachelor's degree:wkly_study_hours10-May        -0.134 0.893586    
## parent_educhigh school:wkly_study_hours10-May               0.685 0.493705    
## parent_educmaster's degree:wkly_study_hours10-May           1.612 0.107887    
## parent_educsome college:wkly_study_hours10-May              1.039 0.299622    
## parent_educsome high school:wkly_study_hours10-May         -0.280 0.780011    
## parent_educbachelor's degree:writing_score                 -1.856 0.064355 .  
## parent_educhigh school:writing_score                       -1.020 0.308492    
## parent_educmaster's degree:writing_score                   -2.460 0.014385 *  
## parent_educsome college:writing_score                      -0.480 0.631416    
## parent_educsome high school:writing_score                  -1.051 0.293963    
## parent_educbachelor's degree:reading_score                  1.740 0.082710 .  
## parent_educhigh school:reading_score                        0.570 0.568913    
## parent_educmaster's degree:reading_score                    2.059 0.040300 *  
## parent_educsome college:reading_score                       0.084 0.933380    
## parent_educsome high school:reading_score                   0.570 0.568830    
## lunch_typestandard:test_prepnone                            0.618 0.536924    
## lunch_typestandard:parent_marital_statusmarried             0.218 0.827725    
## lunch_typestandard:parent_marital_statussingle              0.543 0.587557    
## lunch_typestandard:parent_marital_statuswidowed            -1.164 0.245130    
## lunch_typestandard:practice_sportregularly                  1.283 0.200316    
## lunch_typestandard:practice_sportsometimes                  0.391 0.695702    
## lunch_typestandard:is_first_childyes                        2.068 0.039393 *  
## lunch_typestandard:transport_meansschool_bus                0.662 0.508173    
## lunch_typestandard:wkly_study_hours> 10                    -0.485 0.628036    
## lunch_typestandard:wkly_study_hours10-May                   0.375 0.707742    
## lunch_typestandard:writing_score                            0.208 0.835531    
## lunch_typestandard:reading_score                           -0.519 0.604202    
## test_prepnone:parent_marital_statusmarried                  1.874 0.061832 .  
## test_prepnone:parent_marital_statussingle                   1.848 0.065462 .  
## test_prepnone:parent_marital_statuswidowed                 -1.352 0.177347    
## test_prepnone:practice_sportregularly                       0.238 0.811650    
## test_prepnone:practice_sportsometimes                      -0.036 0.971586    
## test_prepnone:is_first_childyes                            -0.069 0.945083    
## test_prepnone:transport_meansschool_bus                    -2.745 0.006369 ** 
## test_prepnone:wkly_study_hours> 10                         -0.782 0.435008    
## test_prepnone:wkly_study_hours10-May                       -0.293 0.770034    
## test_prepnone:writing_score                                -0.014 0.988446    
## test_prepnone:reading_score                                -0.114 0.909263    
## parent_marital_statusmarried:practice_sportregularly        1.243 0.214712    
## parent_marital_statussingle:practice_sportregularly         2.112 0.035399 *  
## parent_marital_statuswidowed:practice_sportregularly        0.978 0.328579    
## parent_marital_statusmarried:practice_sportsometimes        1.164 0.245333    
## parent_marital_statussingle:practice_sportsometimes         1.569 0.117694    
## parent_marital_statuswidowed:practice_sportsometimes           NA       NA    
## parent_marital_statusmarried:is_first_childyes              1.170 0.242783    
## parent_marital_statussingle:is_first_childyes               1.178 0.239780    
## parent_marital_statuswidowed:is_first_childyes              1.132 0.258577    
## parent_marital_statusmarried:transport_meansschool_bus      0.532 0.595274    
## parent_marital_statussingle:transport_meansschool_bus      -0.662 0.508693    
## parent_marital_statuswidowed:transport_meansschool_bus     -1.752 0.080714 .  
## parent_marital_statusmarried:wkly_study_hours> 10          -0.718 0.473070    
## parent_marital_statussingle:wkly_study_hours> 10           -1.241 0.215645    
## parent_marital_statuswidowed:wkly_study_hours> 10              NA       NA    
## parent_marital_statusmarried:wkly_study_hours10-May        -1.433 0.152689    
## parent_marital_statussingle:wkly_study_hours10-May         -1.082 0.280033    
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## parent_marital_statusmarried:writing_score                  0.374 0.708758    
## parent_marital_statussingle:writing_score                  -0.274 0.784501    
## parent_marital_statuswidowed:writing_score                     NA       NA    
## parent_marital_statusmarried:reading_score                 -0.321 0.748055    
## parent_marital_statussingle:reading_score                   0.373 0.709131    
## parent_marital_statuswidowed:reading_score                     NA       NA    
## practice_sportregularly:is_first_childyes                   1.149 0.251288    
## practice_sportsometimes:is_first_childyes                   0.871 0.384468    
## practice_sportregularly:transport_meansschool_bus           0.201 0.841180    
## practice_sportsometimes:transport_meansschool_bus          -0.400 0.689403    
## practice_sportregularly:wkly_study_hours> 10               -0.860 0.390152    
## practice_sportsometimes:wkly_study_hours> 10               -0.768 0.442771    
## practice_sportregularly:wkly_study_hours10-May              0.099 0.920944    
## practice_sportsometimes:wkly_study_hours10-May              0.508 0.611465    
## practice_sportregularly:writing_score                       0.440 0.659926    
## practice_sportsometimes:writing_score                       0.908 0.364518    
## practice_sportregularly:reading_score                      -0.631 0.528629    
## practice_sportsometimes:reading_score                      -1.099 0.272484    
## is_first_childyes:transport_meansschool_bus                -1.814 0.070594 .  
## is_first_childyes:wkly_study_hours> 10                      0.009 0.993148    
## is_first_childyes:wkly_study_hours10-May                   -1.899 0.058371 .  
## is_first_childyes:writing_score                            -0.321 0.748256    
## is_first_childyes:reading_score                             0.590 0.555819    
## transport_meansschool_bus:wkly_study_hours> 10              1.135 0.257075    
## transport_meansschool_bus:wkly_study_hours10-May            0.762 0.446327    
## transport_meansschool_bus:writing_score                    -0.633 0.527221    
## transport_meansschool_bus:reading_score                    -0.077 0.938720    
## wkly_study_hours> 10:writing_score                         -1.358 0.175384    
## wkly_study_hours10-May:writing_score                       -1.800 0.072815 .  
## wkly_study_hours> 10:reading_score                          1.897 0.058696 .  
## wkly_study_hours10-May:reading_score                        2.379 0.017930 *  
## writing_score:reading_score                                 0.767 0.443789    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.476 on 340 degrees of freedom
## Multiple R-squared:  0.9334, Adjusted R-squared:  0.8846 
## F-statistic: 19.13 on 249 and 340 DF,  p-value: < 2.2e-16
stepwise_model_math2 <- step(full_fit_math2, direction = "both", trace = 1)
## Start:  AIC=2181.24
## math_score ~ (gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score)^2
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:practice_sport             10    154.57 10350 2170.1
## - ethnic_group:parent_marital_status      8     94.75 10290 2170.7
## - ethnic_group:wkly_study_hours           8    107.40 10303 2171.4
## - ethnic_group:lunch_type                 4      9.02 10204 2173.8
## - gender:parent_educ                      5     55.21 10251 2174.4
## - ethnic_group:practice_sport             8    160.52 10356 2174.5
## - ethnic_group:transport_means            4     53.67 10249 2176.3
## - practice_sport:wkly_study_hours         4     56.41 10252 2176.5
## - parent_educ:parent_marital_status      11    302.90 10498 2176.5
## - gender:parent_marital_status            2      1.95 10197 2177.4
## - gender:practice_sport                   2      2.03 10197 2177.4
## - ethnic_group:parent_educ               20    645.97 10841 2177.5
## - gender:wkly_study_hours                 2      6.99 10202 2177.7
## - test_prep:practice_sport                2      7.42 10203 2177.7
## - lunch_type:parent_marital_status        2     10.68 10206 2177.9
## - ethnic_group:test_prep                  4     81.99 10277 2178.0
## - test_prep:wkly_study_hours              2     19.22 10215 2178.4
## - lunch_type:wkly_study_hours             2     22.66 10218 2178.6
## - parent_marital_status:writing_score     2     22.90 10218 2178.6
## - gender:ethnic_group                     4     93.55 10289 2178.6
## - parent_marital_status:reading_score     2     28.08 10224 2178.9
## - practice_sport:transport_means          2     31.09 10226 2179.0
## - test_prep:writing_score                 1      0.01 10195 2179.2
## - gender:is_first_child                   1      0.12 10196 2179.2
## - test_prep:is_first_child                1      0.14 10196 2179.2
## - transport_means:reading_score           1      0.18 10196 2179.3
## - test_prep:reading_score                 1      0.39 10196 2179.3
## - practice_sport:writing_score            2     35.61 10231 2179.3
## - lunch_type:writing_score                1      1.29 10197 2179.3
## - parent_educ:wkly_study_hours           10    318.24 10514 2179.4
## - is_first_child:writing_score            1      3.09 10198 2179.4
## - parent_marital_status:wkly_study_hours  4    107.62 10303 2179.4
## - gender:lunch_type                       1      3.95 10199 2179.5
## - transport_means:wkly_study_hours        2     40.69 10236 2179.6
## - gender:reading_score                    1      6.72 10202 2179.6
## - practice_sport:is_first_child           2     42.00 10237 2179.7
## - gender:test_prep                        1      7.46 10203 2179.7
## - lunch_type:reading_score                1      8.07 10204 2179.7
## - practice_sport:reading_score            2     43.56 10239 2179.8
## - is_first_child:reading_score            1     10.43 10206 2179.8
## - parent_marital_status:is_first_child    2     45.92 10241 2179.9
## - lunch_type:test_prep                    1     11.46 10207 2179.9
## - transport_means:writing_score           1     12.01 10207 2179.9
## - lunch_type:transport_means              1     13.16 10208 2180.0
## - gender:transport_means                  1     14.70 10210 2180.1
## - writing_score:reading_score             1     17.63 10213 2180.3
## - gender:writing_score                    1     22.59 10218 2180.6
## <none>                                                10195 2181.2
## - parent_marital_status:transport_means   2     74.61 10270 2181.6
## - lunch_type:practice_sport               2     86.55 10282 2182.2
## - parent_educ:test_prep                   5    198.51 10394 2182.6
## - parent_marital_status:practice_sport    4    165.02 10360 2182.7
## - wkly_study_hours:writing_score          2    106.46 10302 2183.4
## - parent_educ:transport_means             5    213.35 10409 2183.5
## - parent_educ:reading_score               5    223.98 10419 2184.1
## - test_prep:parent_marital_status         2    120.05 10315 2184.2
## - parent_educ:lunch_type                  5    232.17 10428 2184.5
## - ethnic_group:is_first_child             4    200.96 10396 2184.8
## - parent_educ:is_first_child              5    237.74 10433 2184.8
## - is_first_child:transport_means          1     98.65 10294 2184.9
## - is_first_child:wkly_study_hours         2    143.60 10339 2185.5
## - ethnic_group:writing_score              4    215.09 10410 2185.6
## - lunch_type:is_first_child               1    128.24 10324 2186.6
## - parent_educ:writing_score               5    270.10 10466 2186.7
## - ethnic_group:reading_score              4    239.36 10435 2186.9
## - wkly_study_hours:reading_score          2    191.60 10387 2188.2
## - test_prep:transport_means               1    225.98 10421 2192.2
## 
## Step:  AIC=2170.12
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:parent_educ + gender:lunch_type + 
##     gender:test_prep + gender:parent_marital_status + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:writing_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + ethnic_group:reading_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:wkly_study_hours + parent_educ:writing_score + 
##     parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_marital_status      8    107.27 10457 2160.2
## - ethnic_group:wkly_study_hours           8    112.50 10462 2160.5
## - ethnic_group:lunch_type                 4     12.16 10362 2162.8
## - ethnic_group:practice_sport             8    168.40 10518 2163.6
## - gender:parent_educ                      5     77.32 10427 2164.5
## - practice_sport:wkly_study_hours         4     58.99 10409 2165.5
## - ethnic_group:transport_means            4     69.53 10420 2166.1
## - ethnic_group:parent_educ               20    650.72 11001 2166.1
## - gender:practice_sport                   2      1.17 10351 2166.2
## - parent_educ:parent_marital_status      11    323.23 10673 2166.3
## - gender:parent_marital_status            2      3.78 10354 2166.3
## - gender:wkly_study_hours                 2     10.91 10361 2166.7
## - lunch_type:parent_marital_status        2     11.55 10362 2166.8
## - parent_marital_status:writing_score     2     12.85 10363 2166.8
## - ethnic_group:test_prep                  4     83.54 10434 2166.9
## - parent_marital_status:reading_score     2     14.61 10365 2166.9
## - test_prep:wkly_study_hours              2     15.41 10365 2167.0
## - test_prep:practice_sport                2     18.72 10369 2167.2
## - lunch_type:wkly_study_hours             2     22.79 10373 2167.4
## - gender:ethnic_group                     4     94.95 10445 2167.5
## - practice_sport:transport_means          2     28.70 10379 2167.8
## - transport_means:reading_score           1      0.23 10350 2168.1
## - test_prep:reading_score                 1      0.53 10350 2168.2
## - transport_means:wkly_study_hours        2     36.17 10386 2168.2
## - test_prep:is_first_child                1      1.05 10351 2168.2
## - gender:is_first_child                   1      1.45 10351 2168.2
## - lunch_type:writing_score                1      2.00 10352 2168.2
## - test_prep:writing_score                 1      2.15 10352 2168.2
## - gender:reading_score                    1      2.16 10352 2168.2
## - gender:lunch_type                       1      2.53 10352 2168.3
## - is_first_child:writing_score            1      2.92 10353 2168.3
## - parent_educ:wkly_study_hours           10    323.76 10674 2168.3
## - practice_sport:writing_score            2     40.63 10391 2168.4
## - practice_sport:is_first_child           2     41.06 10391 2168.5
## - parent_marital_status:wkly_study_hours  4    114.38 10464 2168.6
## - parent_marital_status:is_first_child    2     44.64 10395 2168.7
## - gender:test_prep                        1      9.73 10360 2168.7
## - lunch_type:reading_score                1     10.62 10361 2168.7
## - is_first_child:reading_score            1     10.86 10361 2168.7
## - gender:writing_score                    1     14.56 10364 2168.9
## - lunch_type:transport_means              1     18.61 10369 2169.2
## - lunch_type:test_prep                    1     19.05 10369 2169.2
## - transport_means:writing_score           1     19.51 10370 2169.2
## - gender:transport_means                  1     22.93 10373 2169.4
## - practice_sport:reading_score            2     58.48 10408 2169.4
## - writing_score:reading_score             1     27.67 10378 2169.7
## - parent_marital_status:transport_means   2     68.02 10418 2170.0
## <none>                                                10350 2170.1
## - parent_educ:test_prep                   5    193.22 10543 2171.0
## - parent_educ:transport_means             5    200.04 10550 2171.4
## - parent_marital_status:practice_sport    4    166.92 10517 2171.6
## - lunch_type:practice_sport               2    108.18 10458 2172.3
## - wkly_study_hours:writing_score          2    111.81 10462 2172.5
## - test_prep:parent_marital_status         2    120.91 10471 2173.0
## - is_first_child:transport_means          1    101.56 10452 2173.9
## - ethnic_group:writing_score              4    210.66 10561 2174.0
## - ethnic_group:is_first_child             4    211.44 10561 2174.1
## - is_first_child:wkly_study_hours         2    142.36 10492 2174.2
## - parent_educ:is_first_child              5    258.69 10609 2174.7
## - parent_educ:reading_score               5    259.54 10610 2174.7
## - ethnic_group:reading_score              4    230.59 10580 2175.1
## - parent_educ:lunch_type                  5    272.42 10622 2175.4
## - lunch_type:is_first_child               1    151.78 10502 2176.7
## - parent_educ:writing_score               5    296.38 10646 2176.8
## - wkly_study_hours:reading_score          2    198.71 10549 2177.3
## - test_prep:transport_means               1    209.35 10559 2179.9
## + parent_educ:practice_sport             10    154.57 10195 2181.2
## 
## Step:  AIC=2160.21
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:parent_educ + gender:lunch_type + 
##     gender:test_prep + gender:parent_marital_status + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:writing_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:wkly_study_hours           8    115.77 10573 2150.7
## - parent_educ:parent_marital_status      14    366.34 10824 2152.5
## - ethnic_group:lunch_type                 4     17.66 10475 2153.2
## - gender:parent_educ                      5     76.11 10533 2154.5
## - ethnic_group:practice_sport             8    191.15 10648 2154.9
## - practice_sport:wkly_study_hours         4     63.45 10521 2155.8
## - gender:practice_sport                   2      1.58 10459 2156.3
## - gender:parent_marital_status            2      2.03 10459 2156.3
## - gender:wkly_study_hours                 2      9.51 10467 2156.7
## - ethnic_group:transport_means            4     83.66 10541 2156.9
## - ethnic_group:parent_educ               20    673.42 11131 2157.0
## - test_prep:wkly_study_hours              2     17.68 10475 2157.2
## - lunch_type:parent_marital_status        2     19.71 10477 2157.3
## - lunch_type:wkly_study_hours             2     20.46 10478 2157.4
## - practice_sport:transport_means          2     21.51 10479 2157.4
## - ethnic_group:test_prep                  4     96.31 10554 2157.6
## - test_prep:practice_sport                2     27.33 10484 2157.8
## - gender:ethnic_group                     4    100.33 10558 2157.8
## - transport_means:reading_score           1      0.05 10457 2158.2
## - test_prep:reading_score                 1      0.30 10458 2158.2
## - parent_marital_status:is_first_child    2     36.34 10494 2158.2
## - test_prep:writing_score                 1      0.95 10458 2158.3
## - parent_marital_status:writing_score     2     36.81 10494 2158.3
## - parent_marital_status:reading_score     2     37.04 10494 2158.3
## - lunch_type:writing_score                1      1.82 10459 2158.3
## - gender:lunch_type                       1      2.23 10460 2158.3
## - gender:is_first_child                   1      2.25 10460 2158.3
## - transport_means:wkly_study_hours        2     38.11 10495 2158.3
## - is_first_child:writing_score            1      3.64 10461 2158.4
## - gender:reading_score                    1      4.07 10461 2158.4
## - test_prep:is_first_child                1      6.46 10464 2158.6
## - gender:test_prep                        1      7.87 10465 2158.7
## - practice_sport:is_first_child           2     45.38 10503 2158.8
## - is_first_child:reading_score            1     10.84 10468 2158.8
## - parent_marital_status:transport_means   2     46.49 10504 2158.8
## - lunch_type:reading_score                1     11.00 10468 2158.8
## - parent_educ:wkly_study_hours           10    335.36 10793 2158.8
## - practice_sport:writing_score            2     49.45 10507 2159.0
## - transport_means:writing_score           1     15.99 10473 2159.1
## - gender:transport_means                  1     16.03 10473 2159.1
## - gender:writing_score                    1     18.53 10476 2159.2
## - lunch_type:transport_means              1     20.76 10478 2159.4
## - lunch_type:test_prep                    1     23.90 10481 2159.6
## - writing_score:reading_score             1     26.79 10484 2159.7
## <none>                                                10457 2160.2
## - practice_sport:reading_score            2     78.43 10536 2160.6
## - parent_educ:test_prep                   5    186.74 10644 2160.7
## - lunch_type:practice_sport               2    100.64 10558 2161.9
## - parent_educ:transport_means             5    210.27 10668 2161.9
## - parent_marital_status:practice_sport    4    177.54 10635 2162.1
## - wkly_study_hours:writing_score          2    111.12 10568 2162.4
## - parent_marital_status:wkly_study_hours  5    231.47 10689 2163.1
## - is_first_child:wkly_study_hours         2    127.09 10584 2163.3
## - test_prep:parent_marital_status         2    127.24 10584 2163.3
## - ethnic_group:writing_score              4    213.25 10670 2164.1
## - ethnic_group:reading_score              4    221.34 10679 2164.6
## - parent_educ:reading_score               5    263.70 10721 2164.9
## - is_first_child:transport_means          1    123.82 10581 2165.2
## - parent_educ:is_first_child              5    270.93 10728 2165.3
## - parent_educ:lunch_type                  5    274.15 10731 2165.5
## - ethnic_group:is_first_child             4    239.12 10696 2165.6
## - parent_educ:writing_score               5    298.78 10756 2166.8
## - lunch_type:is_first_child               1    156.72 10614 2167.0
## - wkly_study_hours:reading_score          2    203.94 10661 2167.6
## - test_prep:transport_means               1    210.66 10668 2170.0
## + ethnic_group:parent_marital_status      8    107.27 10350 2170.1
## + parent_educ:practice_sport             10    167.09 10290 2170.7
## 
## Step:  AIC=2150.7
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:parent_educ + gender:lunch_type + 
##     gender:test_prep + gender:parent_marital_status + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:writing_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:writing_score + ethnic_group:reading_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:wkly_study_hours + parent_educ:writing_score + 
##     parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:parent_marital_status      14    370.44 10943 2143.0
## - ethnic_group:lunch_type                 4     21.84 10595 2143.9
## - gender:parent_educ                      5     78.71 10652 2145.1
## - ethnic_group:practice_sport             8    190.18 10763 2145.2
## - practice_sport:wkly_study_hours         4     62.38 10635 2146.2
## - parent_educ:wkly_study_hours           10    287.57 10861 2146.5
## - gender:parent_marital_status            2      2.35 10575 2146.8
## - gender:practice_sport                   2      2.97 10576 2146.9
## - ethnic_group:transport_means            4     75.16 10648 2146.9
## - gender:wkly_study_hours                 2     10.89 10584 2147.3
## - ethnic_group:parent_educ               20    677.80 11251 2147.4
## - test_prep:practice_sport                2     19.80 10593 2147.8
## - ethnic_group:test_prep                  4     99.04 10672 2148.2
## - practice_sport:transport_means          2     27.58 10601 2148.2
## - lunch_type:parent_marital_status        2     28.20 10601 2148.3
## - parent_marital_status:is_first_child    2     28.78 10602 2148.3
## - lunch_type:wkly_study_hours             2     30.20 10603 2148.4
## - test_prep:wkly_study_hours              2     35.62 10609 2148.7
## - test_prep:reading_score                 1      0.04 10573 2148.7
## - transport_means:reading_score           1      0.05 10573 2148.7
## - test_prep:writing_score                 1      0.28 10573 2148.7
## - lunch_type:writing_score                1      1.12 10574 2148.8
## - is_first_child:writing_score            1      1.91 10575 2148.8
## - gender:lunch_type                       1      2.40 10575 2148.8
## - gender:reading_score                    1      3.09 10576 2148.9
## - practice_sport:writing_score            2     39.76 10613 2148.9
## - gender:ethnic_group                     4    112.46 10685 2148.9
## - is_first_child:reading_score            1      6.13 10579 2149.0
## - gender:is_first_child                   1      6.77 10580 2149.1
## - lunch_type:reading_score                1      8.11 10581 2149.2
## - gender:test_prep                        1      8.31 10581 2149.2
## - transport_means:wkly_study_hours        2     44.84 10618 2149.2
## - test_prep:is_first_child                1      9.07 10582 2149.2
## - parent_marital_status:reading_score     2     46.76 10620 2149.3
## - parent_marital_status:writing_score     2     47.34 10620 2149.3
## - gender:writing_score                    1     16.37 10589 2149.6
## - lunch_type:transport_means              1     16.90 10590 2149.6
## - parent_marital_status:transport_means   2     53.05 10626 2149.7
## - gender:transport_means                  1     17.94 10591 2149.7
## - practice_sport:is_first_child           2     55.39 10628 2149.8
## - transport_means:writing_score           1     20.63 10594 2149.8
## - writing_score:reading_score             1     25.11 10598 2150.1
## - lunch_type:test_prep                    1     26.64 10600 2150.2
## - practice_sport:reading_score            2     68.07 10641 2150.5
## <none>                                                10573 2150.7
## - parent_educ:test_prep                   5    190.39 10763 2151.2
## - parent_educ:transport_means             5    195.37 10768 2151.5
## - lunch_type:practice_sport               2    104.46 10677 2152.5
## - wkly_study_hours:writing_score          2    105.40 10678 2152.6
## - parent_marital_status:wkly_study_hours  5    214.86 10788 2152.6
## - parent_marital_status:practice_sport    4    189.90 10763 2153.2
## - is_first_child:wkly_study_hours         2    125.83 10699 2153.7
## - parent_educ:reading_score               5    247.50 10820 2154.3
## - ethnic_group:writing_score              4    213.57 10787 2154.5
## - ethnic_group:reading_score              4    222.91 10796 2155.0
## - is_first_child:transport_means          1    114.90 10688 2155.1
## - test_prep:parent_marital_status         2    158.65 10732 2155.5
## - ethnic_group:is_first_child             4    239.71 10813 2155.9
## - parent_educ:lunch_type                  5    277.05 10850 2156.0
## - parent_educ:writing_score               5    287.71 10861 2156.5
## - parent_educ:is_first_child              5    304.57 10878 2157.5
## - wkly_study_hours:reading_score          2    201.97 10775 2157.9
## - lunch_type:is_first_child               1    182.27 10755 2158.8
## + ethnic_group:wkly_study_hours           8    115.77 10457 2160.2
## - test_prep:transport_means               1    213.41 10786 2160.5
## + ethnic_group:parent_marital_status      8    110.54 10462 2160.5
## + parent_educ:practice_sport             10    171.31 10402 2161.1
## 
## Step:  AIC=2143.02
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:parent_educ + gender:lunch_type + 
##     gender:test_prep + gender:parent_marital_status + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:writing_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:writing_score + ethnic_group:reading_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:lunch_type                 4     19.69 10963 2136.1
## - gender:parent_educ                      5     60.12 11004 2136.2
## - ethnic_group:practice_sport             8    183.97 11127 2136.9
## - practice_sport:wkly_study_hours         4     55.26 10999 2138.0
## - parent_educ:wkly_study_hours           10    286.28 11230 2138.3
## - ethnic_group:transport_means            4     69.53 11013 2138.8
## - parent_marital_status:is_first_child    3     33.22 10977 2138.8
## - parent_marital_status:reading_score     3     38.18 10982 2139.1
## - parent_marital_status:writing_score     3     39.30 10983 2139.1
## - gender:practice_sport                   2      3.65 10947 2139.2
## - gender:wkly_study_hours                 2      3.66 10947 2139.2
## - gender:parent_marital_status            3     52.07 10996 2139.8
## - lunch_type:parent_marital_status        2     21.75 10965 2140.2
## - gender:ethnic_group                     4     96.94 11040 2140.2
## - practice_sport:transport_means          2     28.74 10972 2140.6
## - test_prep:practice_sport                2     31.50 10975 2140.7
## - transport_means:reading_score           1      0.01 10943 2141.0
## - test_prep:writing_score                 1      0.01 10943 2141.0
## - lunch_type:writing_score                1      0.06 10944 2141.0
## - test_prep:reading_score                 1      0.27 10944 2141.0
## - gender:reading_score                    1      0.30 10944 2141.0
## - practice_sport:writing_score            2     39.08 10982 2141.1
## - lunch_type:reading_score                1      2.26 10946 2141.1
## - is_first_child:writing_score            1      3.34 10947 2141.2
## - gender:test_prep                        1      4.08 10948 2141.2
## - parent_educ:test_prep                   5    153.84 11097 2141.3
## - gender:transport_means                  1      4.61 10948 2141.3
## - gender:lunch_type                       1      4.68 10948 2141.3
## - practice_sport:is_first_child           2     42.51 10986 2141.3
## - lunch_type:transport_means              1      5.58 10949 2141.3
## - gender:is_first_child                   1      5.66 10949 2141.3
## - test_prep:wkly_study_hours              2     45.33 10989 2141.5
## - ethnic_group:test_prep                  4    120.21 11064 2141.5
## - test_prep:is_first_child                1      8.97 10952 2141.5
## - is_first_child:reading_score            1      9.60 10953 2141.5
## - gender:writing_score                    1      9.68 10953 2141.5
## - lunch_type:wkly_study_hours             2     47.89 10991 2141.6
## - lunch_type:test_prep                    1     11.05 10954 2141.6
## - transport_means:writing_score           1     14.54 10958 2141.8
## - parent_marital_status:wkly_study_hours  6    203.84 11147 2141.9
## - transport_means:wkly_study_hours        2     54.04 10998 2141.9
## - ethnic_group:parent_educ               20    748.41 11692 2142.1
## - writing_score:reading_score             1     20.63 10964 2142.1
## - parent_educ:transport_means             5    174.89 11118 2142.4
## - practice_sport:reading_score            2     64.53 11008 2142.5
## - parent_marital_status:transport_means   3    106.69 11050 2142.7
## <none>                                                10943 2143.0
## - wkly_study_hours:writing_score          2     95.34 11039 2144.1
## - parent_marital_status:practice_sport    5    209.74 11153 2144.2
## - lunch_type:practice_sport               2    105.82 11049 2144.7
## - parent_educ:reading_score               5    227.48 11171 2145.2
## - ethnic_group:writing_score              4    208.08 11152 2146.1
## - is_first_child:wkly_study_hours         2    132.78 11076 2146.1
## - ethnic_group:reading_score              4    217.79 11161 2146.7
## - parent_educ:lunch_type                  5    259.62 11203 2146.8
## - parent_educ:writing_score               5    269.83 11213 2147.4
## - test_prep:parent_marital_status         3    198.36 11142 2147.6
## - parent_educ:is_first_child              5    278.62 11222 2147.8
## - is_first_child:transport_means          1    135.60 11079 2148.3
## - ethnic_group:is_first_child             4    254.47 11198 2148.6
## - wkly_study_hours:reading_score          2    184.42 11128 2148.9
## + parent_educ:parent_marital_status      14    370.44 10573 2150.7
## - test_prep:transport_means               1    185.79 11129 2150.9
## + parent_educ:practice_sport             10    195.29 10748 2152.4
## - lunch_type:is_first_child               1    213.24 11157 2152.4
## + ethnic_group:wkly_study_hours           8    119.87 10824 2152.5
## + ethnic_group:parent_marital_status     11    160.05 10783 2156.3
## 
## Step:  AIC=2136.08
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:parent_educ + gender:lunch_type + 
##     gender:test_prep + gender:parent_marital_status + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:writing_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:test_prep + ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:wkly_study_hours + parent_educ:writing_score + 
##     parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_educ                      5     62.87 11026 2129.4
## - ethnic_group:practice_sport             8    184.53 11148 2129.9
## - practice_sport:wkly_study_hours         4     53.51 11017 2130.9
## - parent_educ:wkly_study_hours           10    286.33 11250 2131.3
## - parent_marital_status:is_first_child    3     31.01 10994 2131.8
## - parent_marital_status:reading_score     3     35.51 10999 2132.0
## - ethnic_group:transport_means            4     73.49 11037 2132.0
## - parent_marital_status:writing_score     3     36.21 10999 2132.0
## - gender:practice_sport                   2      4.42 10968 2132.3
## - gender:wkly_study_hours                 2      4.81 10968 2132.3
## - gender:parent_marital_status            3     52.97 11016 2132.9
## - lunch_type:parent_marital_status        2     19.33 10982 2133.1
## - practice_sport:transport_means          2     23.09 10986 2133.3
## - test_prep:practice_sport                2     30.62 10994 2133.7
## - practice_sport:writing_score            2     36.99 11000 2134.1
## - test_prep:writing_score                 1      0.01 10963 2134.1
## - gender:reading_score                    1      0.07 10963 2134.1
## - transport_means:reading_score           1      0.16 10963 2134.1
## - test_prep:reading_score                 1      0.24 10963 2134.1
## - lunch_type:reading_score                1      0.61 10964 2134.1
## - lunch_type:writing_score                1      0.89 10964 2134.1
## - practice_sport:is_first_child           2     38.45 11002 2134.2
## - ethnic_group:test_prep                  4    113.36 11076 2134.2
## - gender:ethnic_group                     4    113.89 11077 2134.2
## - is_first_child:writing_score            1      2.37 10966 2134.2
## - gender:test_prep                        1      3.11 10966 2134.2
## - gender:transport_means                  1      4.34 10968 2134.3
## - parent_educ:test_prep                   5    154.24 11117 2134.3
## - gender:is_first_child                   1      4.61 10968 2134.3
## - lunch_type:transport_means              1      5.45 10969 2134.4
## - gender:lunch_type                       1      6.71 10970 2134.4
## - test_prep:is_first_child                1      6.79 10970 2134.4
## - lunch_type:test_prep                    1      7.47 10971 2134.5
## - is_first_child:reading_score            1      8.64 10972 2134.6
## - gender:writing_score                    1      8.65 10972 2134.6
## - transport_means:writing_score           1     11.42 10974 2134.7
## - test_prep:wkly_study_hours              2     51.20 11014 2134.8
## - parent_marital_status:wkly_study_hours  6    201.69 11165 2134.8
## - lunch_type:wkly_study_hours             2     52.44 11016 2134.9
## - transport_means:wkly_study_hours        2     55.07 11018 2135.0
## - parent_educ:transport_means             5    168.90 11132 2135.1
## - writing_score:reading_score             1     19.62 10983 2135.1
## - practice_sport:reading_score            2     60.53 11024 2135.3
## - parent_marital_status:transport_means   3    108.97 11072 2135.9
## <none>                                                10963 2136.1
## - ethnic_group:parent_educ               20    778.61 11742 2136.6
## - wkly_study_hours:writing_score          2     89.42 11052 2136.9
## - lunch_type:practice_sport               2    102.29 11065 2137.6
## - parent_marital_status:practice_sport    5    219.27 11182 2137.8
## - parent_educ:reading_score               5    227.21 11190 2138.2
## - is_first_child:wkly_study_hours         2    131.30 11094 2139.1
## - parent_educ:lunch_type                  5    264.42 11228 2140.1
## - ethnic_group:writing_score              4    227.60 11191 2140.2
## - ethnic_group:reading_score              4    228.81 11192 2140.3
## - test_prep:parent_marital_status         3    195.00 11158 2140.5
## - parent_educ:writing_score               5    271.51 11235 2140.5
## - parent_educ:is_first_child              5    274.93 11238 2140.7
## - wkly_study_hours:reading_score          2    177.34 11140 2141.6
## - is_first_child:transport_means          1    149.76 11113 2142.1
## + ethnic_group:lunch_type                 4     19.69 10943 2143.0
## - ethnic_group:is_first_child             4    281.19 11244 2143.0
## + parent_educ:parent_marital_status      14    368.29 10595 2143.9
## - test_prep:transport_means               1    185.07 11148 2144.0
## + parent_educ:practice_sport             10    204.69 10758 2145.0
## - lunch_type:is_first_child               1    209.37 11172 2145.2
## + ethnic_group:wkly_study_hours           8    121.96 10841 2145.5
## + ethnic_group:parent_marital_status     11    170.18 10793 2148.8
## 
## Step:  AIC=2129.45
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:wkly_study_hours + parent_educ:writing_score + 
##     parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:practice_sport             8    179.30 11205 2123.0
## - parent_educ:wkly_study_hours           10    257.64 11284 2123.1
## - practice_sport:wkly_study_hours         4     48.74 11075 2124.1
## - parent_marital_status:is_first_child    3     28.03 11054 2124.9
## - parent_marital_status:reading_score     3     33.12 11059 2125.2
## - ethnic_group:transport_means            4     70.69 11097 2125.2
## - parent_marital_status:writing_score     3     33.82 11060 2125.3
## - gender:wkly_study_hours                 2      3.40 11029 2125.6
## - gender:practice_sport                   2      8.55 11034 2125.9
## - gender:parent_marital_status            3     51.57 11078 2126.2
## - lunch_type:parent_marital_status        2     15.07 11041 2126.3
## - practice_sport:transport_means          2     22.97 11049 2126.7
## - test_prep:practice_sport                2     24.29 11050 2126.8
## - gender:ethnic_group                     4    101.48 11128 2126.9
## - ethnic_group:test_prep                  4    111.34 11137 2127.4
## - transport_means:reading_score           1      0.00 11026 2127.4
## - gender:reading_score                    1      0.00 11026 2127.4
## - test_prep:writing_score                 1      0.06 11026 2127.5
## - lunch_type:reading_score                1      0.11 11026 2127.5
## - parent_educ:test_prep                   5    150.67 11177 2127.5
## - test_prep:reading_score                 1      0.36 11026 2127.5
## - gender:test_prep                        1      0.58 11027 2127.5
## - lunch_type:transport_means              1      2.29 11028 2127.6
## - is_first_child:writing_score            1      3.44 11029 2127.6
## - lunch_type:writing_score                1      3.60 11030 2127.7
## - gender:is_first_child                   1      3.94 11030 2127.7
## - gender:transport_means                  1      5.35 11031 2127.7
## - practice_sport:is_first_child           2     43.27 11069 2127.8
## - gender:writing_score                    1      7.05 11033 2127.8
## - lunch_type:test_prep                    1      8.42 11034 2127.9
## - lunch_type:wkly_study_hours             2     46.06 11072 2127.9
## - test_prep:is_first_child                1      8.66 11035 2127.9
## - gender:lunch_type                       1      8.67 11035 2127.9
## - parent_marital_status:wkly_study_hours  6    199.53 11226 2128.0
## - is_first_child:reading_score            1     12.89 11039 2128.1
## - transport_means:writing_score           1     14.98 11041 2128.3
## - writing_score:reading_score             1     15.45 11042 2128.3
## - practice_sport:writing_score            2     54.11 11080 2128.3
## - test_prep:wkly_study_hours              2     59.03 11085 2128.6
## - transport_means:wkly_study_hours        2     61.70 11088 2128.8
## - parent_educ:transport_means             5    179.76 11206 2129.0
## - parent_marital_status:transport_means   3    109.99 11136 2129.3
## <none>                                                11026 2129.4
## - practice_sport:reading_score            2     76.33 11102 2129.5
## - wkly_study_hours:writing_score          2     86.04 11112 2130.0
## - ethnic_group:parent_educ               20    785.45 11811 2130.1
## - parent_marital_status:practice_sport    5    213.89 11240 2130.8
## - parent_educ:reading_score               5    222.34 11248 2131.2
## - lunch_type:practice_sport               2    112.70 11139 2131.4
## - parent_educ:lunch_type                  5    244.91 11271 2132.4
## - is_first_child:wkly_study_hours         2    141.62 11168 2133.0
## - test_prep:parent_marital_status         3    184.77 11211 2133.3
## - parent_educ:is_first_child              5    266.96 11293 2133.6
## - parent_educ:writing_score               5    267.14 11293 2133.6
## - ethnic_group:writing_score              4    246.35 11272 2134.5
## - ethnic_group:reading_score              4    246.69 11273 2134.5
## - wkly_study_hours:reading_score          2    173.45 11199 2134.7
## - is_first_child:transport_means          1    155.00 11181 2135.7
## + gender:parent_educ                      5     62.87 10963 2136.1
## + ethnic_group:lunch_type                 4     22.45 11004 2136.2
## - test_prep:transport_means               1    178.33 11204 2136.9
## - ethnic_group:is_first_child             4    296.29 11322 2137.1
## + parent_educ:practice_sport             10    220.71 10805 2137.5
## + parent_educ:parent_marital_status      14    351.50 10674 2138.3
## - lunch_type:is_first_child               1    208.52 11234 2138.5
## + ethnic_group:wkly_study_hours           8    128.37 10898 2138.6
## + ethnic_group:parent_marital_status     11    177.45 10849 2141.9
## 
## Step:  AIC=2122.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:writing_score + ethnic_group:reading_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:wkly_study_hours           10    230.83 11436 2115.0
## - practice_sport:wkly_study_hours         4     44.47 11250 2117.3
## - parent_marital_status:is_first_child    3     24.44 11230 2118.3
## - ethnic_group:transport_means            4     65.46 11271 2118.4
## - parent_marital_status:reading_score     3     35.90 11241 2118.9
## - parent_marital_status:writing_score     3     37.94 11243 2119.0
## - gender:wkly_study_hours                 2      1.40 11207 2119.1
## - gender:practice_sport                   2      6.08 11211 2119.3
## - test_prep:practice_sport                2     17.82 11223 2119.9
## - gender:parent_marital_status            3     58.81 11264 2120.1
## - practice_sport:transport_means          2     22.02 11227 2120.1
## - gender:ethnic_group                     4     98.81 11304 2120.2
## - practice_sport:is_first_child           2     25.68 11231 2120.3
## - ethnic_group:test_prep                  4    104.55 11310 2120.4
## - lunch_type:parent_marital_status        2     28.85 11234 2120.5
## - parent_marital_status:wkly_study_hours  6    182.31 11388 2120.5
## - transport_means:wkly_study_hours        2     34.57 11240 2120.8
## - gender:reading_score                    1      0.05 11205 2121.0
## - lunch_type:reading_score                1      0.07 11205 2121.0
## - test_prep:writing_score                 1      0.18 11206 2121.0
## - transport_means:reading_score           1      0.28 11206 2121.0
## - lunch_type:transport_means              1      0.98 11206 2121.0
## - test_prep:reading_score                 1      1.17 11206 2121.0
## - lunch_type:writing_score                1      1.52 11207 2121.1
## - is_first_child:writing_score            1      1.80 11207 2121.1
## - gender:transport_means                  1      1.88 11207 2121.1
## - gender:test_prep                        1      2.52 11208 2121.1
## - lunch_type:wkly_study_hours             2     42.37 11248 2121.2
## - test_prep:is_first_child                1      4.71 11210 2121.2
## - gender:is_first_child                   1      6.04 11211 2121.3
## - gender:lunch_type                       1      8.69 11214 2121.4
## - is_first_child:reading_score            1      9.22 11214 2121.5
## - transport_means:writing_score           1      9.35 11215 2121.5
## - gender:writing_score                    1     11.33 11217 2121.6
## - lunch_type:test_prep                    1     11.49 11217 2121.6
## - parent_educ:test_prep                   5    165.53 11371 2121.6
## - writing_score:reading_score             1     12.47 11218 2121.6
## - parent_marital_status:transport_means   3     91.34 11297 2121.8
## - test_prep:wkly_study_hours              2     60.16 11266 2122.1
## - parent_educ:transport_means             5    175.32 11381 2122.1
## <none>                                                11205 2123.0
## - wkly_study_hours:writing_score          2     83.69 11289 2123.4
## - practice_sport:writing_score            2     85.78 11291 2123.5
## - ethnic_group:parent_educ               20    798.88 12004 2123.6
## - parent_marital_status:practice_sport    5    205.09 11410 2123.7
## - lunch_type:practice_sport               2     93.39 11299 2123.9
## - parent_educ:reading_score               5    209.40 11415 2123.9
## - practice_sport:reading_score            2    101.88 11307 2124.3
## - ethnic_group:writing_score              4    179.45 11385 2124.3
## - ethnic_group:reading_score              4    183.50 11389 2124.6
## - test_prep:parent_marital_status         3    154.76 11360 2125.1
## - parent_educ:lunch_type                  5    237.66 11443 2125.3
## - parent_educ:writing_score               5    247.17 11452 2125.8
## - is_first_child:wkly_study_hours         2    135.04 11340 2126.0
## - parent_educ:is_first_child              5    266.59 11472 2126.8
## - ethnic_group:is_first_child             4    251.10 11456 2128.1
## - wkly_study_hours:reading_score          2    174.15 11380 2128.1
## + ethnic_group:practice_sport             8    179.30 11026 2129.4
## - test_prep:transport_means               1    163.77 11369 2129.5
## + ethnic_group:lunch_type                 4     23.02 11182 2129.8
## + gender:parent_educ                      5     57.64 11148 2129.9
## - lunch_type:is_first_child               1    174.65 11380 2130.1
## - is_first_child:transport_means          1    185.99 11391 2130.7
## + parent_educ:practice_sport             10    214.52 10991 2131.6
## + ethnic_group:wkly_study_hours           8    123.23 11082 2132.4
## + parent_educ:parent_marital_status      14    341.14 10864 2132.7
## + ethnic_group:parent_marital_status     11    192.32 11013 2134.8
## 
## Step:  AIC=2115
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     ethnic_group:writing_score + ethnic_group:reading_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:transport_means            4     52.35 11488 2109.7
## - practice_sport:wkly_study_hours         4     54.01 11490 2109.8
## - parent_marital_status:is_first_child    3     16.54 11453 2109.9
## - parent_marital_status:reading_score     3     26.93 11463 2110.4
## - parent_marital_status:writing_score     3     32.31 11468 2110.7
## - gender:practice_sport                   2      2.67 11439 2111.1
## - gender:wkly_study_hours                 2      4.62 11441 2111.2
## - test_prep:practice_sport                2     11.63 11448 2111.6
## - gender:ethnic_group                     4     90.60 11527 2111.7
## - gender:parent_marital_status            3     55.37 11492 2111.8
## - practice_sport:transport_means          2     19.82 11456 2112.0
## - transport_means:wkly_study_hours        2     20.22 11456 2112.0
## - ethnic_group:test_prep                  4    100.86 11537 2112.2
## - practice_sport:is_first_child           2     23.61 11460 2112.2
## - parent_marital_status:wkly_study_hours  6    184.78 11621 2112.5
## - parent_marital_status:transport_means   3     68.39 11504 2112.5
## - lunch_type:parent_marital_status        2     36.35 11472 2112.9
## - parent_educ:lunch_type                  5    155.03 11591 2112.9
## - lunch_type:reading_score                1      0.02 11436 2113.0
## - lunch_type:transport_means              1      0.08 11436 2113.0
## - transport_means:reading_score           1      0.42 11437 2113.0
## - lunch_type:writing_score                1      1.08 11437 2113.1
## - gender:reading_score                    1      1.36 11438 2113.1
## - gender:lunch_type                       1      1.45 11438 2113.1
## - gender:test_prep                        1      1.61 11438 2113.1
## - gender:transport_means                  1      1.84 11438 2113.1
## - test_prep:writing_score                 1      2.20 11438 2113.1
## - is_first_child:writing_score            1      2.24 11438 2113.1
## - test_prep:wkly_study_hours              2     41.29 11477 2113.1
## - test_prep:is_first_child                1      2.70 11439 2113.1
## - test_prep:reading_score                 1      4.88 11441 2113.2
## - parent_educ:test_prep                   5    162.30 11598 2113.3
## - gender:is_first_child                   1      6.36 11442 2113.3
## - wkly_study_hours:writing_score          2     46.01 11482 2113.4
## - transport_means:writing_score           1      7.18 11443 2113.4
## - lunch_type:test_prep                    1     10.81 11447 2113.6
## - is_first_child:reading_score            1     11.16 11447 2113.6
## - parent_educ:transport_means             5    169.09 11605 2113.7
## - ethnic_group:parent_educ               20    778.97 12215 2113.9
## - writing_score:reading_score             1     17.40 11454 2113.9
## - gender:writing_score                    1     23.31 11459 2114.2
## - practice_sport:writing_score            2     71.19 11507 2114.7
## - parent_marital_status:practice_sport    5    190.27 11626 2114.7
## - lunch_type:wkly_study_hours             2     74.79 11511 2114.8
## <none>                                                11436 2115.0
## - practice_sport:reading_score            2     79.80 11516 2115.1
## - parent_educ:reading_score               5    206.11 11642 2115.5
## - lunch_type:practice_sport               2     92.27 11528 2115.7
## - ethnic_group:reading_score              4    174.40 11610 2115.9
## - ethnic_group:writing_score              4    176.12 11612 2116.0
## - parent_educ:writing_score               5    221.50 11658 2116.3
## - is_first_child:wkly_study_hours         2    110.02 11546 2116.7
## - wkly_study_hours:reading_score          2    123.52 11560 2117.3
## - test_prep:parent_marital_status         3    165.15 11601 2117.5
## - parent_educ:is_first_child              5    253.03 11689 2117.9
## - ethnic_group:is_first_child             4    239.94 11676 2119.2
## - test_prep:transport_means               1    153.18 11589 2120.8
## - is_first_child:transport_means          1    167.96 11604 2121.6
## + ethnic_group:lunch_type                 4     21.00 11415 2121.9
## + parent_educ:wkly_study_hours           10    230.83 11205 2123.0
## + gender:parent_educ                      5     38.20 11398 2123.0
## + ethnic_group:practice_sport             8    152.49 11284 2123.1
## - lunch_type:is_first_child               1    211.45 11648 2123.8
## + parent_educ:practice_sport             10    193.99 11242 2124.9
## + parent_educ:parent_marital_status      14    328.12 11108 2125.8
## + ethnic_group:parent_marital_status     11    208.81 11227 2126.1
## + ethnic_group:wkly_study_hours           8     77.96 11358 2127.0
## 
## Step:  AIC=2109.7
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:wkly_study_hours         4     56.16 11545 2104.6
## - parent_marital_status:is_first_child    3     19.14 11508 2104.7
## - parent_marital_status:reading_score     3     29.62 11518 2105.2
## - parent_marital_status:writing_score     3     35.02 11524 2105.5
## - gender:practice_sport                   2      3.44 11492 2105.9
## - gender:wkly_study_hours                 2      3.96 11492 2105.9
## - gender:parent_marital_status            3     49.54 11538 2106.2
## - test_prep:practice_sport                2     12.00 11500 2106.3
## - parent_marital_status:wkly_study_hours  6    171.23 11660 2106.4
## - gender:ethnic_group                     4     92.92 11581 2106.4
## - parent_marital_status:transport_means   3     56.50 11545 2106.6
## - practice_sport:is_first_child           2     17.93 11506 2106.6
## - practice_sport:transport_means          2     18.20 11507 2106.6
## - transport_means:wkly_study_hours        2     27.28 11516 2107.1
## - lunch_type:parent_marital_status        2     33.00 11522 2107.4
## - lunch_type:transport_means              1      0.01 11488 2107.7
## - ethnic_group:test_prep                  4    117.50 11606 2107.7
## - lunch_type:reading_score                1      0.23 11489 2107.7
## - gender:lunch_type                       1      0.25 11489 2107.7
## - test_prep:writing_score                 1      0.45 11489 2107.7
## - gender:reading_score                    1      1.11 11490 2107.8
## - gender:transport_means                  1      1.51 11490 2107.8
## - transport_means:reading_score           1      1.80 11490 2107.8
## - lunch_type:writing_score                1      1.85 11490 2107.8
## - test_prep:reading_score                 1      2.13 11491 2107.8
## - parent_educ:transport_means             5    159.05 11648 2107.8
## - gender:test_prep                        1      2.48 11491 2107.8
## - parent_educ:test_prep                   5    160.44 11649 2107.9
## - test_prep:wkly_study_hours              2     42.98 11532 2107.9
## - transport_means:writing_score           1      3.98 11492 2107.9
## - test_prep:is_first_child                1      4.41 11493 2107.9
## - is_first_child:writing_score            1      5.20 11494 2108.0
## - gender:is_first_child                   1      6.16 11495 2108.0
## - wkly_study_hours:writing_score          2     48.70 11537 2108.2
## - parent_educ:lunch_type                  5    167.65 11656 2108.2
## - writing_score:reading_score             1     13.50 11502 2108.4
## - lunch_type:test_prep                    1     14.35 11503 2108.4
## - is_first_child:reading_score            1     17.58 11506 2108.6
## - ethnic_group:parent_educ               20    787.62 12276 2108.8
## - gender:writing_score                    1     24.28 11513 2108.9
## - lunch_type:wkly_study_hours             2     70.36 11559 2109.3
## - parent_marital_status:practice_sport    5    189.71 11678 2109.4
## - parent_educ:reading_score               5    195.94 11684 2109.7
## <none>                                                11488 2109.7
## - practice_sport:writing_score            2     78.54 11567 2109.7
## - practice_sport:reading_score            2     88.67 11577 2110.2
## - parent_educ:writing_score               5    212.17 11701 2110.5
## - is_first_child:wkly_study_hours         2    103.37 11592 2111.0
## - lunch_type:practice_sport               2    104.84 11593 2111.1
## - ethnic_group:reading_score              4    186.85 11675 2111.2
## - ethnic_group:writing_score              4    189.57 11678 2111.3
## - test_prep:parent_marital_status         3    162.30 11651 2112.0
## - wkly_study_hours:reading_score          2    129.77 11618 2112.3
## - parent_educ:is_first_child              5    250.08 11739 2112.4
## - ethnic_group:is_first_child             4    245.84 11734 2114.2
## + ethnic_group:transport_means            4     52.35 11436 2115.0
## - test_prep:transport_means               1    146.39 11635 2115.2
## - is_first_child:transport_means          1    165.15 11654 2116.1
## + ethnic_group:lunch_type                 4     25.77 11463 2116.4
## + gender:parent_educ                      5     34.75 11454 2117.9
## + ethnic_group:practice_sport             8    147.41 11341 2118.1
## + parent_educ:wkly_study_hours           10    217.73 11271 2118.4
## - lunch_type:is_first_child               1    214.06 11702 2118.6
## + parent_educ:practice_sport             10    211.18 11277 2118.8
## + ethnic_group:parent_marital_status     11    218.43 11270 2120.4
## + parent_educ:parent_marital_status      14    316.32 11172 2121.2
## + ethnic_group:wkly_study_hours           8     74.34 11414 2121.9
## 
## Step:  AIC=2104.57
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:reading_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:is_first_child    3     18.64 11563 2099.5
## - parent_marital_status:wkly_study_hours  6    154.99 11700 2100.4
## - parent_marital_status:reading_score     3     40.15 11585 2100.6
## - parent_marital_status:transport_means   3     40.94 11586 2100.7
## - gender:wkly_study_hours                 2      2.89 11548 2100.7
## - parent_marital_status:writing_score     3     46.61 11591 2100.9
## - gender:practice_sport                   2      8.86 11554 2101.0
## - gender:ethnic_group                     4     88.58 11633 2101.1
## - test_prep:practice_sport                2     11.67 11556 2101.2
## - gender:parent_marital_status            3     53.78 11598 2101.3
## - ethnic_group:parent_educ               20    745.11 12290 2101.5
## - practice_sport:is_first_child           2     18.65 11563 2101.5
## - practice_sport:transport_means          2     19.02 11564 2101.6
## - transport_means:wkly_study_hours        2     19.75 11564 2101.6
## - parent_educ:test_prep                   5    149.37 11694 2102.2
## - ethnic_group:test_prep                  4    113.10 11658 2102.3
## - lunch_type:parent_marital_status        2     36.59 11581 2102.4
## - lunch_type:transport_means              1      0.03 11545 2102.6
## - lunch_type:reading_score                1      0.33 11545 2102.6
## - gender:lunch_type                       1      0.55 11545 2102.6
## - gender:transport_means                  1      0.67 11545 2102.6
## - test_prep:writing_score                 1      0.89 11546 2102.6
## - gender:reading_score                    1      1.15 11546 2102.6
## - transport_means:reading_score           1      1.56 11546 2102.7
## - lunch_type:writing_score                1      1.97 11547 2102.7
## - test_prep:is_first_child                1      1.98 11547 2102.7
## - gender:test_prep                        1      1.99 11547 2102.7
## - parent_educ:transport_means             5    159.65 11704 2102.7
## - test_prep:reading_score                 1      2.52 11547 2102.7
## - test_prep:wkly_study_hours              2     41.99 11587 2102.7
## - is_first_child:writing_score            1      3.58 11548 2102.8
## - transport_means:writing_score           1      4.63 11549 2102.8
## - gender:is_first_child                   1      5.24 11550 2102.8
## - lunch_type:test_prep                    1      9.92 11555 2103.1
## - parent_educ:lunch_type                  5    171.28 11716 2103.3
## - writing_score:reading_score             1     14.72 11559 2103.3
## - wkly_study_hours:writing_score          2     55.18 11600 2103.4
## - is_first_child:reading_score            1     16.11 11561 2103.4
## - parent_educ:reading_score               5    183.39 11728 2103.9
## - gender:writing_score                    1     25.52 11570 2103.9
## - parent_marital_status:practice_sport    5    185.07 11730 2104.0
## - lunch_type:wkly_study_hours             2     67.58 11612 2104.0
## <none>                                                11545 2104.6
## - practice_sport:writing_score            2     80.97 11626 2104.7
## - parent_educ:writing_score               5    200.47 11745 2104.7
## - practice_sport:reading_score            2     89.10 11634 2105.1
## - ethnic_group:reading_score              4    170.74 11715 2105.2
## - ethnic_group:writing_score              4    175.80 11720 2105.5
## - lunch_type:practice_sport               2    101.07 11646 2105.7
## - is_first_child:wkly_study_hours         2    105.32 11650 2105.9
## - test_prep:parent_marital_status         3    154.65 11699 2106.4
## - parent_educ:is_first_child              5    237.09 11782 2106.6
## - wkly_study_hours:reading_score          2    145.17 11690 2107.9
## - ethnic_group:is_first_child             4    246.91 11792 2109.1
## - test_prep:transport_means               1    139.51 11684 2109.7
## + practice_sport:wkly_study_hours         4     56.16 11488 2109.7
## + ethnic_group:transport_means            4     54.50 11490 2109.8
## + ethnic_group:lunch_type                 4     23.53 11521 2111.4
## - is_first_child:transport_means          1    175.41 11720 2111.5
## - lunch_type:is_first_child               1    193.31 11738 2112.4
## + parent_educ:wkly_study_hours           10    225.81 11319 2112.9
## + gender:parent_educ                      5     31.18 11514 2113.0
## + parent_educ:practice_sport             10    223.69 11321 2113.0
## + ethnic_group:practice_sport             8    141.96 11403 2113.3
## + ethnic_group:parent_marital_status     11    223.08 11322 2115.1
## + parent_educ:parent_marital_status      14    323.97 11221 2115.8
## + ethnic_group:wkly_study_hours           8     72.25 11472 2116.9
## 
## Step:  AIC=2099.53
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     parent_marital_status:reading_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:reading_score     3     37.94 11601 2095.5
## - gender:wkly_study_hours                 2      1.56 11565 2095.6
## - parent_marital_status:writing_score     3     40.91 11604 2095.6
## - gender:practice_sport                   2      8.86 11572 2096.0
## - test_prep:practice_sport                2      9.47 11573 2096.0
## - gender:ethnic_group                     4     89.11 11652 2096.1
## - ethnic_group:parent_educ               20    745.94 12309 2096.4
## - parent_marital_status:transport_means   3     58.11 11621 2096.5
## - practice_sport:transport_means          2     19.92 11583 2096.5
## - transport_means:wkly_study_hours        2     20.64 11584 2096.6
## - practice_sport:is_first_child           2     22.99 11586 2096.7
## - parent_marital_status:wkly_study_hours  6    184.33 11748 2096.9
## - parent_educ:test_prep                   5    149.70 11713 2097.1
## - lunch_type:parent_marital_status        2     37.84 11601 2097.4
## - lunch_type:transport_means              1      0.00 11563 2097.5
## - gender:transport_means                  1      0.49 11564 2097.6
## - ethnic_group:test_prep                  4    118.75 11682 2097.6
## - lunch_type:reading_score                1      0.75 11564 2097.6
## - test_prep:writing_score                 1      0.95 11564 2097.6
## - gender:reading_score                    1      1.13 11564 2097.6
## - gender:lunch_type                       1      1.21 11564 2097.6
## - gender:test_prep                        1      1.34 11565 2097.6
## - transport_means:reading_score           1      1.64 11565 2097.6
## - test_prep:is_first_child                1      2.27 11566 2097.6
## - test_prep:reading_score                 1      2.53 11566 2097.7
## - lunch_type:writing_score                1      2.60 11566 2097.7
## - test_prep:wkly_study_hours              2     42.69 11606 2097.7
## - parent_educ:lunch_type                  5    161.67 11725 2097.7
## - is_first_child:writing_score            1      4.10 11567 2097.7
## - transport_means:writing_score           1      4.85 11568 2097.8
## - gender:is_first_child                   1      6.08 11569 2097.8
## - lunch_type:test_prep                    1      8.34 11572 2097.9
## - writing_score:reading_score             1     14.24 11578 2098.2
## - parent_educ:transport_means             5    172.34 11736 2098.2
## - wkly_study_hours:writing_score          2     54.80 11618 2098.3
## - is_first_child:reading_score            1     18.57 11582 2098.5
## - parent_educ:reading_score               5    178.06 11741 2098.5
## - gender:writing_score                    1     24.52 11588 2098.8
## - gender:parent_marital_status            3    105.47 11669 2098.9
## - lunch_type:wkly_study_hours             2     70.19 11634 2099.1
## - parent_marital_status:practice_sport    5    191.26 11754 2099.2
## - parent_educ:writing_score               5    193.51 11757 2099.3
## <none>                                                11563 2099.5
## - practice_sport:writing_score            2     82.36 11646 2099.7
## - practice_sport:reading_score            2     89.45 11653 2100.1
## - ethnic_group:reading_score              4    170.41 11734 2100.2
## - ethnic_group:writing_score              4    175.89 11739 2100.4
## - lunch_type:practice_sport               2     96.71 11660 2100.4
## - parent_educ:is_first_child              5    235.26 11798 2101.4
## - is_first_child:wkly_study_hours         2    120.77 11684 2101.7
## - test_prep:parent_marital_status         3    162.52 11726 2101.8
## - wkly_study_hours:reading_score          2    145.19 11708 2102.9
## - ethnic_group:is_first_child             4    249.85 11813 2104.1
## - test_prep:transport_means               1    137.93 11701 2104.5
## + parent_marital_status:is_first_child    3     18.64 11545 2104.6
## + ethnic_group:transport_means            4     56.96 11506 2104.6
## + practice_sport:wkly_study_hours         4     55.66 11508 2104.7
## + ethnic_group:lunch_type                 4     21.03 11542 2106.4
## - is_first_child:transport_means          1    191.03 11754 2107.2
## - lunch_type:is_first_child               1    196.21 11760 2107.4
## + gender:parent_educ                      5     28.74 11534 2108.1
## + parent_educ:practice_sport             10    220.48 11343 2108.2
## + parent_educ:wkly_study_hours           10    216.00 11347 2108.4
## + ethnic_group:practice_sport             8    136.76 11426 2108.5
## + ethnic_group:parent_marital_status     11    218.20 11345 2110.3
## + ethnic_group:wkly_study_hours           8     68.51 11495 2112.0
## + parent_educ:parent_marital_status      15    331.78 11232 2112.3
## 
## Step:  AIC=2095.46
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:writing_score     3     14.06 11615 2090.2
## - gender:wkly_study_hours                 2      2.17 11603 2091.6
## - gender:ethnic_group                     4     85.71 11687 2091.8
## - gender:practice_sport                   2      9.38 11611 2091.9
## - test_prep:practice_sport                2     11.09 11612 2092.0
## - ethnic_group:parent_educ               20    744.19 12345 2092.1
## - practice_sport:transport_means          2     15.66 11617 2092.2
## - parent_marital_status:transport_means   3     55.37 11657 2092.3
## - practice_sport:is_first_child           2     19.31 11620 2092.4
## - parent_marital_status:wkly_study_hours  6    178.85 11780 2092.5
## - transport_means:wkly_study_hours        2     22.41 11624 2092.6
## - parent_educ:test_prep                   5    147.26 11748 2092.9
## - lunch_type:parent_marital_status        2     37.74 11639 2093.4
## - test_prep:wkly_study_hours              2     38.75 11640 2093.4
## - ethnic_group:test_prep                  4    118.79 11720 2093.5
## - lunch_type:transport_means              1      0.40 11602 2093.5
## - lunch_type:reading_score                1      0.56 11602 2093.5
## - test_prep:writing_score                 1      0.65 11602 2093.5
## - gender:lunch_type                       1      0.70 11602 2093.5
## - gender:reading_score                    1      0.88 11602 2093.5
## - test_prep:reading_score                 1      1.77 11603 2093.6
## - gender:test_prep                        1      1.89 11603 2093.6
## - transport_means:reading_score           1      2.10 11603 2093.6
## - lunch_type:writing_score                1      2.30 11604 2093.6
## - gender:transport_means                  1      2.46 11604 2093.6
## - is_first_child:writing_score            1      3.51 11605 2093.6
## - parent_educ:lunch_type                  5    162.06 11763 2093.6
## - test_prep:is_first_child                1      4.08 11605 2093.7
## - transport_means:writing_score           1      4.82 11606 2093.7
## - gender:is_first_child                   1      5.35 11607 2093.7
## - wkly_study_hours:writing_score          2     44.97 11646 2093.7
## - lunch_type:test_prep                    1      7.15 11608 2093.8
## - writing_score:reading_score             1     16.47 11618 2094.3
## - is_first_child:reading_score            1     17.24 11618 2094.3
## - parent_educ:reading_score               5    177.65 11779 2094.4
## - parent_marital_status:practice_sport    5    179.16 11780 2094.5
## - gender:writing_score                    1     23.44 11625 2094.7
## - gender:parent_marital_status            3    103.77 11705 2094.7
## - lunch_type:wkly_study_hours             2     65.57 11667 2094.8
## - parent_educ:transport_means             5    189.84 11791 2095.0
## - parent_educ:writing_score               5    190.36 11792 2095.1
## <none>                                                11601 2095.5
## - practice_sport:writing_score            2     82.85 11684 2095.7
## - practice_sport:reading_score            2     95.57 11697 2096.3
## - ethnic_group:reading_score              4    182.96 11784 2096.7
## - ethnic_group:writing_score              4    188.32 11790 2097.0
## - lunch_type:practice_sport               2    113.33 11715 2097.2
## - parent_educ:is_first_child              5    236.26 11838 2097.3
## - test_prep:parent_marital_status         3    158.72 11760 2097.5
## - is_first_child:wkly_study_hours         2    121.09 11722 2097.6
## - wkly_study_hours:reading_score          2    131.21 11732 2098.1
## + parent_marital_status:reading_score     3     37.94 11563 2099.5
## + practice_sport:wkly_study_hours         4     64.78 11536 2100.2
## - ethnic_group:is_first_child             4    253.99 11855 2100.2
## - test_prep:transport_means               1    138.45 11740 2100.5
## + ethnic_group:transport_means            4     57.10 11544 2100.6
## + parent_marital_status:is_first_child    3     16.43 11585 2100.6
## + ethnic_group:lunch_type                 4     21.38 11580 2102.4
## - lunch_type:is_first_child               1    195.87 11797 2103.3
## - is_first_child:transport_means          1    197.63 11799 2103.4
## + gender:parent_educ                      5     24.55 11577 2104.2
## + ethnic_group:practice_sport             8    136.95 11464 2104.4
## + parent_educ:wkly_study_hours           10    210.88 11390 2104.6
## + parent_educ:practice_sport             10    194.67 11407 2105.5
## + ethnic_group:parent_marital_status     11    222.81 11378 2106.0
## + ethnic_group:wkly_study_hours           8     72.84 11528 2107.7
## + parent_educ:parent_marital_status      15    246.29 11355 2112.8
## 
## Step:  AIC=2090.17
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:wkly_study_hours                 2      1.90 11617 2086.3
## - gender:ethnic_group                     4     85.99 11701 2086.5
## - gender:practice_sport                   2      9.40 11625 2086.7
## - ethnic_group:parent_educ               20    742.41 12358 2086.7
## - test_prep:practice_sport                2     11.44 11627 2086.8
## - parent_marital_status:transport_means   3     51.32 11667 2086.8
## - practice_sport:transport_means          2     13.53 11629 2086.9
## - practice_sport:is_first_child           2     20.48 11636 2087.2
## - parent_educ:test_prep                   5    139.91 11755 2087.2
## - transport_means:wkly_study_hours        2     22.45 11638 2087.3
## - parent_marital_status:wkly_study_hours  6    191.78 11807 2087.8
## - test_prep:wkly_study_hours              2     39.62 11655 2088.2
## - lunch_type:transport_means              1      0.27 11616 2088.2
## - lunch_type:reading_score                1      0.46 11616 2088.2
## - gender:lunch_type                       1      0.72 11616 2088.2
## - test_prep:writing_score                 1      0.77 11616 2088.2
## - gender:reading_score                    1      1.27 11617 2088.2
## - ethnic_group:test_prep                  4    120.10 11735 2088.2
## - transport_means:reading_score           1      1.70 11617 2088.3
## - test_prep:reading_score                 1      1.71 11617 2088.3
## - gender:transport_means                  1      2.20 11618 2088.3
## - gender:test_prep                        1      2.31 11618 2088.3
## - lunch_type:writing_score                1      2.33 11618 2088.3
## - lunch_type:parent_marital_status        2     43.27 11659 2088.4
## - test_prep:is_first_child                1      4.07 11619 2088.4
## - is_first_child:writing_score            1      4.17 11620 2088.4
## - transport_means:writing_score           1      5.08 11620 2088.4
## - gender:is_first_child                   1      5.66 11621 2088.5
## - wkly_study_hours:writing_score          2     45.32 11661 2088.5
## - lunch_type:test_prep                    1      6.55 11622 2088.5
## - parent_educ:lunch_type                  5    168.67 11784 2088.7
## - is_first_child:reading_score            1     18.65 11634 2089.1
## - gender:parent_marital_status            3     98.91 11714 2089.2
## - parent_educ:reading_score               5    180.15 11795 2089.2
## - writing_score:reading_score             1     22.76 11638 2089.3
## - gender:writing_score                    1     24.71 11640 2089.4
## - lunch_type:wkly_study_hours             2     64.45 11680 2089.4
## - parent_marital_status:practice_sport    5    188.37 11804 2089.7
## - parent_educ:transport_means             5    189.17 11804 2089.7
## - parent_educ:writing_score               5    192.00 11807 2089.8
## <none>                                                11615 2090.2
## - practice_sport:writing_score            2     79.49 11695 2090.2
## - practice_sport:reading_score            2     94.16 11709 2090.9
## - parent_educ:is_first_child              5    227.45 11843 2091.6
## - ethnic_group:reading_score              4    195.00 11810 2092.0
## - lunch_type:practice_sport               2    116.92 11732 2092.1
## - is_first_child:wkly_study_hours         2    122.20 11738 2092.3
## - ethnic_group:writing_score              4    202.51 11818 2092.4
## - wkly_study_hours:reading_score          2    131.21 11746 2092.8
## - test_prep:parent_marital_status         3    175.70 11791 2093.0
## + practice_sport:wkly_study_hours         4     64.72 11551 2094.9
## - ethnic_group:is_first_child             4    257.50 11873 2095.1
## - test_prep:transport_means               1    137.72 11753 2095.1
## + ethnic_group:transport_means            4     55.50 11560 2095.3
## + parent_marital_status:is_first_child    3     15.57 11600 2095.4
## + parent_marital_status:writing_score     3     14.06 11601 2095.5
## + parent_marital_status:reading_score     3     11.09 11604 2095.6
## + ethnic_group:lunch_type                 4     20.25 11595 2097.1
## - lunch_type:is_first_child               1    198.08 11813 2098.2
## - is_first_child:transport_means          1    203.38 11819 2098.4
## + gender:parent_educ                      5     24.08 11591 2098.9
## + parent_educ:wkly_study_hours           10    214.51 11401 2099.2
## + ethnic_group:practice_sport             8    136.47 11479 2099.2
## + parent_educ:practice_sport             10    198.09 11417 2100.0
## + ethnic_group:parent_marital_status     11    198.75 11416 2102.0
## + ethnic_group:wkly_study_hours           8     71.66 11544 2102.5
## + parent_educ:parent_marital_status      15    233.46 11382 2108.2
## 
## Step:  AIC=2086.27
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:ethnic_group + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:writing_score + ethnic_group:reading_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:ethnic_group                     4     85.24 11702 2082.6
## - gender:practice_sport                   2      9.72 11627 2082.8
## - test_prep:practice_sport                2     11.38 11629 2082.8
## - parent_marital_status:transport_means   3     51.56 11669 2082.9
## - practice_sport:transport_means          2     13.98 11631 2083.0
## - ethnic_group:parent_educ               20    752.15 12369 2083.3
## - practice_sport:is_first_child           2     20.96 11638 2083.3
## - parent_educ:test_prep                   5    140.26 11758 2083.3
## - transport_means:wkly_study_hours        2     22.93 11640 2083.4
## - lunch_type:transport_means              1      0.25 11617 2084.3
## - lunch_type:reading_score                1      0.35 11618 2084.3
## - test_prep:writing_score                 1      0.64 11618 2084.3
## - gender:lunch_type                       1      0.84 11618 2084.3
## - gender:reading_score                    1      1.36 11619 2084.3
## - test_prep:reading_score                 1      1.54 11619 2084.3
## - transport_means:reading_score           1      1.65 11619 2084.3
## - lunch_type:writing_score                1      2.13 11619 2084.4
## - gender:transport_means                  1      2.22 11619 2084.4
## - test_prep:wkly_study_hours              2     41.82 11659 2084.4
## - gender:test_prep                        1      2.73 11620 2084.4
## - ethnic_group:test_prep                  4    121.51 11739 2084.4
## - lunch_type:parent_marital_status        2     42.23 11659 2084.4
## - parent_marital_status:wkly_study_hours  6    202.30 11820 2084.5
## - test_prep:is_first_child                1      3.97 11621 2084.5
## - is_first_child:writing_score            1      4.73 11622 2084.5
## - transport_means:writing_score           1      5.27 11622 2084.5
## - gender:is_first_child                   1      5.85 11623 2084.6
## - lunch_type:test_prep                    1      6.82 11624 2084.6
## - parent_educ:lunch_type                  5    167.40 11785 2084.7
## - wkly_study_hours:writing_score          2     53.00 11670 2085.0
## - is_first_child:reading_score            1     20.01 11637 2085.3
## - writing_score:reading_score             1     22.76 11640 2085.4
## - parent_educ:reading_score               5    182.22 11799 2085.4
## - lunch_type:wkly_study_hours             2     63.49 11681 2085.5
## - gender:parent_marital_status            3    103.73 11721 2085.5
## - gender:writing_score                    1     24.84 11642 2085.5
## - parent_marital_status:practice_sport    5    190.33 11808 2085.9
## - parent_educ:transport_means             5    190.61 11808 2085.9
## - parent_educ:writing_score               5    193.69 11811 2086.0
## <none>                                                11617 2086.3
## - practice_sport:writing_score            2     80.44 11698 2086.3
## - practice_sport:reading_score            2     94.22 11711 2087.0
## - parent_educ:is_first_child              5    225.69 11843 2087.6
## - ethnic_group:reading_score              4    195.64 11813 2088.1
## - lunch_type:practice_sport               2    119.86 11737 2088.3
## - is_first_child:wkly_study_hours         2    122.02 11739 2088.4
## - ethnic_group:writing_score              4    203.54 11821 2088.5
## - test_prep:parent_marital_status         3    174.80 11792 2089.1
## - wkly_study_hours:reading_score          2    140.79 11758 2089.4
## + gender:wkly_study_hours                 2      1.90 11615 2090.2
## + practice_sport:wkly_study_hours         4     63.46 11554 2091.0
## - test_prep:transport_means               1    139.76 11757 2091.3
## + ethnic_group:transport_means            4     54.95 11562 2091.5
## + parent_marital_status:is_first_child    3     14.10 11603 2091.6
## + parent_marital_status:writing_score     3     13.79 11603 2091.6
## - ethnic_group:is_first_child             4    267.25 11884 2091.7
## + parent_marital_status:reading_score     3     10.76 11606 2091.7
## + ethnic_group:lunch_type                 4     20.71 11596 2093.2
## - lunch_type:is_first_child               1    198.87 11816 2094.3
## - is_first_child:transport_means          1    206.12 11823 2094.7
## + gender:parent_educ                      5     24.16 11593 2095.0
## + parent_educ:wkly_study_hours           10    216.08 11401 2095.2
## + ethnic_group:practice_sport             8    135.85 11481 2095.3
## + parent_educ:practice_sport             10    194.10 11423 2096.3
## + ethnic_group:parent_marital_status     11    198.17 11419 2098.1
## + ethnic_group:wkly_study_hours           8     72.34 11545 2098.6
## + parent_educ:parent_marital_status      15    231.61 11386 2104.4
## 
## Step:  AIC=2082.58
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:parent_marital_status + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:writing_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:transport_means          2      8.04 11710 2079.0
## - test_prep:practice_sport                2      8.95 11711 2079.0
## - gender:practice_sport                   2     11.76 11714 2079.2
## - parent_marital_status:transport_means   3     56.96 11759 2079.4
## - transport_means:wkly_study_hours        2     22.02 11724 2079.7
## - practice_sport:is_first_child           2     23.29 11726 2079.8
## - lunch_type:parent_marital_status        2     35.54 11738 2080.4
## - parent_educ:test_prep                   5    155.61 11858 2080.4
## - ethnic_group:test_prep                  4    119.01 11821 2080.6
## - parent_marital_status:wkly_study_hours  6    200.11 11902 2080.6
## - gender:lunch_type                       1      0.10 11702 2080.6
## - lunch_type:reading_score                1      0.18 11703 2080.6
## - lunch_type:transport_means              1      0.32 11703 2080.6
## - test_prep:writing_score                 1      0.36 11703 2080.6
## - test_prep:reading_score                 1      1.06 11704 2080.6
## - lunch_type:writing_score                1      1.41 11704 2080.7
## - gender:transport_means                  1      2.31 11705 2080.7
## - test_prep:wkly_study_hours              2     42.36 11745 2080.7
## - gender:reading_score                    1      3.01 11705 2080.7
## - transport_means:writing_score           1      3.19 11706 2080.7
## - parent_educ:reading_score               5    163.04 11866 2080.8
## - transport_means:reading_score           1      3.63 11706 2080.8
## - is_first_child:writing_score            1      4.25 11707 2080.8
## - gender:is_first_child                   1      4.30 11707 2080.8
## - test_prep:is_first_child                1      4.43 11707 2080.8
## - gender:test_prep                        1      4.66 11707 2080.8
## - lunch_type:test_prep                    1      8.48 11711 2081.0
## - wkly_study_hours:writing_score          2     49.96 11752 2081.1
## - ethnic_group:parent_educ               20    790.68 12493 2081.2
## - parent_educ:transport_means             5    175.76 11878 2081.4
## - parent_educ:lunch_type                  5    175.76 11878 2081.4
## - is_first_child:reading_score            1     19.36 11722 2081.6
## - parent_educ:writing_score               5    181.85 11884 2081.7
## - writing_score:reading_score             1     21.84 11724 2081.7
## - lunch_type:wkly_study_hours             2     63.06 11766 2081.8
## - gender:parent_marital_status            3    108.51 11811 2082.0
## - gender:writing_score                    1     33.87 11736 2082.3
## <none>                                                11702 2082.6
## - parent_marital_status:practice_sport    5    203.21 11906 2082.7
## - ethnic_group:reading_score              4    167.13 11870 2082.9
## - ethnic_group:writing_score              4    168.87 11871 2083.0
## - practice_sport:writing_score            2     89.06 11792 2083.1
## - practice_sport:reading_score            2     99.46 11802 2083.6
## - is_first_child:wkly_study_hours         2    121.58 11824 2084.7
## - parent_educ:is_first_child              5    247.68 11950 2084.9
## - lunch_type:practice_sport               2    128.62 11831 2085.0
## - test_prep:parent_marital_status         3    174.47 11877 2085.3
## - wkly_study_hours:reading_score          2    138.29 11841 2085.5
## + gender:ethnic_group                     4     85.24 11617 2086.3
## + gender:wkly_study_hours                 2      1.15 11701 2086.5
## + ethnic_group:transport_means            4     60.36 11642 2087.5
## + practice_sport:wkly_study_hours         4     59.57 11643 2087.6
## - test_prep:transport_means               1    144.46 11847 2087.8
## + parent_marital_status:is_first_child    3     14.30 11688 2087.9
## + parent_marital_status:writing_score     3     13.99 11688 2087.9
## + parent_marital_status:reading_score     3     11.19 11691 2088.0
## - ethnic_group:is_first_child             4    282.33 11985 2088.7
## + ethnic_group:lunch_type                 4     30.48 11672 2089.0
## - lunch_type:is_first_child               1    211.76 11914 2091.2
## + gender:parent_educ                      5     17.96 11684 2091.7
## - is_first_child:transport_means          1    225.28 11928 2091.8
## + ethnic_group:practice_sport             8    132.88 11570 2091.8
## + parent_educ:wkly_study_hours           10    207.02 11495 2092.1
## + parent_educ:practice_sport             10    195.61 11507 2092.6
## + ethnic_group:parent_marital_status     11    206.85 11496 2094.1
## + ethnic_group:wkly_study_hours           8     80.69 11622 2094.5
## + parent_educ:parent_marital_status      15    226.68 11476 2101.0
## 
## Step:  AIC=2078.99
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:parent_marital_status + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:writing_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score + 
##     parent_marital_status:practice_sport + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:wkly_study_hours + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:practice_sport                2      9.71 11720 2075.5
## - gender:practice_sport                   2     13.24 11724 2075.7
## - parent_marital_status:transport_means   3     58.27 11769 2075.9
## - transport_means:wkly_study_hours        2     21.83 11732 2076.1
## - practice_sport:is_first_child           2     22.58 11733 2076.1
## - lunch_type:parent_marital_status        2     35.22 11746 2076.8
## - ethnic_group:test_prep                  4    117.57 11828 2076.9
## - parent_educ:reading_score               5    158.06 11868 2076.9
## - parent_marital_status:wkly_study_hours  6    200.13 11911 2077.0
## - gender:lunch_type                       1      0.07 11710 2077.0
## - lunch_type:reading_score                1      0.16 11711 2077.0
## - lunch_type:transport_means              1      0.25 11711 2077.0
## - test_prep:writing_score                 1      0.53 11711 2077.0
## - parent_educ:test_prep                   5    160.69 11871 2077.0
## - lunch_type:writing_score                1      1.26 11712 2077.1
## - test_prep:reading_score                 1      1.35 11712 2077.1
## - gender:transport_means                  1      2.23 11713 2077.1
## - transport_means:writing_score           1      2.34 11713 2077.1
## - gender:reading_score                    1      3.06 11714 2077.1
## - is_first_child:writing_score            1      3.79 11714 2077.2
## - test_prep:is_first_child                1      4.04 11714 2077.2
## - gender:is_first_child                   1      4.57 11715 2077.2
## - gender:test_prep                        1      5.05 11716 2077.2
## - transport_means:reading_score           1      5.07 11716 2077.2
## - test_prep:wkly_study_hours              2     46.18 11757 2077.3
## - lunch_type:test_prep                    1      9.03 11720 2077.4
## - wkly_study_hours:writing_score          2     50.83 11761 2077.5
## - parent_educ:transport_means             5    172.56 11883 2077.6
## - parent_educ:writing_score               5    177.42 11888 2077.9
## - is_first_child:reading_score            1     18.85 11729 2077.9
## - parent_educ:lunch_type                  5    179.63 11890 2078.0
## - writing_score:reading_score             1     21.45 11732 2078.1
## - lunch_type:wkly_study_hours             2     61.81 11772 2078.1
## - gender:parent_marital_status            3    105.08 11816 2078.3
## - gender:writing_score                    1     34.65 11745 2078.7
## <none>                                                11710 2079.0
## - parent_marital_status:practice_sport    5    202.74 11913 2079.1
## - ethnic_group:parent_educ               20    825.22 12536 2079.2
## - ethnic_group:reading_score              4    167.15 11878 2079.3
## - ethnic_group:writing_score              4    168.01 11878 2079.4
## - practice_sport:writing_score            2     91.15 11802 2079.6
## - practice_sport:reading_score            2    102.47 11813 2080.1
## - is_first_child:wkly_study_hours         2    123.13 11834 2081.2
## - parent_educ:is_first_child              5    251.54 11962 2081.5
## - lunch_type:practice_sport               2    131.95 11842 2081.6
## - test_prep:parent_marital_status         3    173.50 11884 2081.7
## - wkly_study_hours:reading_score          2    138.10 11849 2081.9
## + practice_sport:transport_means          2      8.04 11702 2082.6
## + gender:wkly_study_hours                 2      1.33 11709 2082.9
## + gender:ethnic_group                     4     79.30 11631 2083.0
## + practice_sport:wkly_study_hours         4     60.11 11650 2083.9
## + ethnic_group:transport_means            4     57.79 11653 2084.1
## - test_prep:transport_means               1    143.38 11854 2084.2
## + parent_marital_status:is_first_child    3     15.82 11695 2084.2
## + parent_marital_status:writing_score     3     12.30 11698 2084.4
## + parent_marital_status:reading_score     3      9.82 11701 2084.5
## - ethnic_group:is_first_child             4    278.94 11989 2084.9
## + ethnic_group:lunch_type                 4     27.32 11683 2085.6
## - lunch_type:is_first_child               1    208.17 11919 2087.4
## + gender:parent_educ                      5     18.25 11692 2088.1
## + ethnic_group:practice_sport             8    130.82 11580 2088.4
## + parent_educ:wkly_study_hours           10    207.46 11503 2088.4
## - is_first_child:transport_means          1    234.59 11945 2088.7
## + parent_educ:practice_sport             10    192.14 11518 2089.2
## + ethnic_group:wkly_study_hours           8     85.60 11625 2090.7
## + ethnic_group:parent_marital_status     11    202.22 11508 2090.7
## + parent_educ:parent_marital_status      15    229.78 11481 2097.3
## 
## Step:  AIC=2075.48
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:parent_marital_status + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:writing_score + gender:reading_score + ethnic_group:parent_educ + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:practice_sport                   2     11.70 11732 2072.1
## - parent_marital_status:transport_means   3     57.34 11778 2072.4
## - practice_sport:is_first_child           2     20.00 11740 2072.5
## - transport_means:wkly_study_hours        2     20.64 11741 2072.5
## - ethnic_group:test_prep                  4    114.46 11835 2073.2
## - lunch_type:parent_marital_status        2     34.55 11755 2073.2
## - parent_educ:reading_score               5    156.39 11877 2073.3
## - parent_educ:test_prep                   5    157.07 11877 2073.3
## - gender:lunch_type                       1      0.04 11720 2073.5
## - lunch_type:transport_means              1      0.17 11720 2073.5
## - lunch_type:reading_score                1      0.34 11720 2073.5
## - parent_marital_status:wkly_study_hours  6    200.89 11921 2073.5
## - lunch_type:writing_score                1      1.63 11722 2073.6
## - transport_means:writing_score           1      1.98 11722 2073.6
## - gender:transport_means                  1      2.20 11722 2073.6
## - test_prep:writing_score                 1      2.24 11722 2073.6
## - gender:reading_score                    1      3.34 11724 2073.7
## - test_prep:reading_score                 1      3.45 11724 2073.7
## - is_first_child:writing_score            1      3.80 11724 2073.7
## - gender:test_prep                        1      4.16 11724 2073.7
## - gender:is_first_child                   1      4.49 11725 2073.7
## - test_prep:is_first_child                1      4.60 11725 2073.7
## - transport_means:reading_score           1      5.64 11726 2073.8
## - test_prep:wkly_study_hours              2     46.32 11766 2073.8
## - lunch_type:test_prep                    1      8.18 11728 2073.9
## - parent_educ:transport_means             5    169.82 11890 2074.0
## - wkly_study_hours:writing_score          2     50.44 11771 2074.0
## - parent_educ:writing_score               5    174.72 11895 2074.2
## - parent_educ:lunch_type                  5    178.56 11899 2074.4
## - is_first_child:reading_score            1     19.11 11739 2074.4
## - writing_score:reading_score             1     19.87 11740 2074.5
## - lunch_type:wkly_study_hours             2     62.66 11783 2074.6
## - gender:parent_marital_status            3    105.20 11825 2074.8
## - gender:writing_score                    1     35.28 11756 2075.2
## <none>                                                11720 2075.5
## - ethnic_group:reading_score              4    161.27 11882 2075.5
## - ethnic_group:writing_score              4    162.95 11883 2075.6
## - parent_marital_status:practice_sport    5    206.37 11927 2075.8
## - ethnic_group:parent_educ               20    836.92 12557 2076.2
## - practice_sport:writing_score            2    109.89 11830 2077.0
## - practice_sport:reading_score            2    111.20 11831 2077.1
## - is_first_child:wkly_study_hours         2    121.95 11842 2077.6
## - parent_educ:is_first_child              5    249.39 11970 2077.9
## - test_prep:parent_marital_status         3    169.22 11889 2077.9
## - wkly_study_hours:reading_score          2    137.85 11858 2078.4
## - lunch_type:practice_sport               2    145.62 11866 2078.8
## + test_prep:practice_sport                2      9.71 11710 2079.0
## + practice_sport:transport_means          2      8.80 11711 2079.0
## + gender:wkly_study_hours                 2      1.29 11719 2079.4
## + gender:ethnic_group                     4     76.47 11644 2079.6
## - test_prep:transport_means               1    139.37 11860 2080.4
## + practice_sport:wkly_study_hours         4     59.42 11661 2080.5
## + ethnic_group:transport_means            4     56.62 11664 2080.6
## + parent_marital_status:is_first_child    3     13.97 11706 2080.8
## + parent_marital_status:writing_score     3     12.30 11708 2080.9
## + parent_marital_status:reading_score     3      9.70 11710 2081.0
## - ethnic_group:is_first_child             4    287.75 12008 2081.8
## + ethnic_group:lunch_type                 4     27.21 11693 2082.1
## - lunch_type:is_first_child               1    211.04 11931 2084.0
## + gender:parent_educ                      5     16.22 11704 2084.7
## + ethnic_group:practice_sport             8    130.05 11590 2084.9
## - is_first_child:transport_means          1    229.99 11950 2084.9
## + parent_educ:wkly_study_hours           10    202.62 11518 2085.2
## + parent_educ:practice_sport             10    196.22 11524 2085.5
## + ethnic_group:parent_marital_status     11    204.85 11515 2087.1
## + ethnic_group:wkly_study_hours           8     81.31 11639 2087.4
## + parent_educ:parent_marital_status      15    234.21 11486 2093.6
## 
## Step:  AIC=2072.07
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:parent_marital_status + 
##     gender:is_first_child + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - transport_means:wkly_study_hours        2     19.87 11752 2069.1
## - practice_sport:is_first_child           2     22.22 11754 2069.2
## - parent_marital_status:transport_means   3     64.19 11796 2069.3
## - lunch_type:parent_marital_status        2     31.98 11764 2069.7
## - ethnic_group:test_prep                  4    116.24 11848 2069.9
## - parent_educ:reading_score               5    157.53 11889 2069.9
## - gender:lunch_type                       1      0.13 11732 2070.1
## - lunch_type:transport_means              1      0.34 11732 2070.1
## - lunch_type:reading_score                1      0.43 11732 2070.1
## - parent_educ:test_prep                   5    162.03 11894 2070.2
## - lunch_type:writing_score                1      1.97 11734 2070.2
## - gender:reading_score                    1      2.32 11734 2070.2
## - test_prep:writing_score                 1      2.41 11734 2070.2
## - gender:transport_means                  1      2.59 11734 2070.2
## - transport_means:writing_score           1      2.60 11734 2070.2
## - test_prep:reading_score                 1      3.55 11735 2070.2
## - gender:test_prep                        1      3.99 11736 2070.3
## - is_first_child:writing_score            1      4.35 11736 2070.3
## - transport_means:reading_score           1      4.74 11737 2070.3
## - parent_educ:transport_means             5    165.33 11897 2070.3
## - test_prep:is_first_child                1      5.69 11738 2070.3
## - gender:is_first_child                   1      5.89 11738 2070.4
## - test_prep:wkly_study_hours              2     46.97 11779 2070.4
## - lunch_type:test_prep                    1      7.86 11740 2070.5
## - parent_marital_status:wkly_study_hours  6    209.27 11941 2070.5
## - parent_educ:writing_score               5    175.27 11907 2070.8
## - parent_educ:lunch_type                  5    175.44 11907 2070.8
## - wkly_study_hours:writing_score          2     56.21 11788 2070.9
## - is_first_child:reading_score            1     19.30 11751 2071.0
## - writing_score:reading_score             1     21.23 11753 2071.1
## - lunch_type:wkly_study_hours             2     61.34 11793 2071.1
## - gender:parent_marital_status            3    106.51 11838 2071.4
## - gender:writing_score                    1     31.50 11763 2071.7
## <none>                                                11732 2072.1
## - ethnic_group:reading_score              4    160.50 11892 2072.1
## - ethnic_group:writing_score              4    163.95 11896 2072.2
## - parent_marital_status:practice_sport    5    213.06 11945 2072.7
## - ethnic_group:parent_educ               20    839.27 12571 2072.8
## - practice_sport:writing_score            2    102.73 11835 2073.2
## - practice_sport:reading_score            2    103.40 11835 2073.2
## - is_first_child:wkly_study_hours         2    121.01 11853 2074.1
## - parent_educ:is_first_child              5    247.43 11979 2074.4
## - test_prep:parent_marital_status         3    176.10 11908 2074.9
## - lunch_type:practice_sport               2    145.50 11877 2075.3
## - wkly_study_hours:reading_score          2    147.77 11880 2075.4
## + gender:practice_sport                   2     11.70 11720 2075.5
## + practice_sport:transport_means          2     10.50 11721 2075.5
## + test_prep:practice_sport                2      8.17 11724 2075.7
## + gender:wkly_study_hours                 2      1.54 11730 2076.0
## + gender:ethnic_group                     4     77.71 11654 2076.2
## + practice_sport:wkly_study_hours         4     66.16 11666 2076.7
## - test_prep:transport_means               1    139.27 11871 2077.0
## + ethnic_group:transport_means            4     59.82 11672 2077.1
## + parent_marital_status:is_first_child    3     15.04 11717 2077.3
## + parent_marital_status:writing_score     3     12.63 11719 2077.4
## + parent_marital_status:reading_score     3     11.30 11721 2077.5
## - ethnic_group:is_first_child             4    289.73 12022 2078.5
## + ethnic_group:lunch_type                 4     26.52 11705 2078.7
## + gender:parent_educ                      5     14.69 11717 2081.3
## + ethnic_group:practice_sport             8    131.24 11601 2081.4
## - is_first_child:transport_means          1    229.18 11961 2081.5
## - lunch_type:is_first_child               1    230.00 11962 2081.5
## + parent_educ:wkly_study_hours           10    203.94 11528 2081.7
## + parent_educ:practice_sport             10    199.48 11532 2081.9
## + ethnic_group:parent_marital_status     11    209.53 11522 2083.4
## + ethnic_group:wkly_study_hours           8     80.42 11652 2084.0
## + parent_educ:parent_marital_status      15    241.64 11490 2089.8
## 
## Step:  AIC=2069.06
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:parent_marital_status + 
##     gender:is_first_child + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:transport_means   3     63.35 11815 2066.2
## - practice_sport:is_first_child           2     23.88 11776 2066.3
## - lunch_type:parent_marital_status        2     29.57 11781 2066.6
## - parent_educ:reading_score               5    159.41 11911 2067.0
## - parent_educ:test_prep                   5    159.51 11911 2067.0
## - parent_educ:transport_means             5    160.45 11912 2067.1
## - gender:lunch_type                       1      0.13 11752 2067.1
## - lunch_type:transport_means              1      0.18 11752 2067.1
## - lunch_type:reading_score                1      0.93 11753 2067.1
## - gender:transport_means                  1      2.17 11754 2067.2
## - test_prep:writing_score                 1      2.78 11754 2067.2
## - lunch_type:writing_score                1      2.88 11755 2067.2
## - ethnic_group:test_prep                  4    123.05 11875 2067.2
## - test_prep:wkly_study_hours              2     42.89 11795 2067.2
## - transport_means:writing_score           1      3.13 11755 2067.2
## - gender:reading_score                    1      3.98 11756 2067.3
## - parent_marital_status:wkly_study_hours  6    205.06 11957 2067.3
## - gender:test_prep                        1      4.12 11756 2067.3
## - test_prep:reading_score                 1      4.18 11756 2067.3
## - transport_means:reading_score           1      4.25 11756 2067.3
## - is_first_child:writing_score            1      4.82 11757 2067.3
## - test_prep:is_first_child                1      5.44 11757 2067.3
## - lunch_type:test_prep                    1      6.04 11758 2067.4
## - gender:is_first_child                   1      8.23 11760 2067.5
## - lunch_type:wkly_study_hours             2     54.53 11806 2067.8
## - wkly_study_hours:writing_score          2     56.62 11808 2067.9
## - parent_educ:writing_score               5    179.81 11932 2068.0
## - is_first_child:reading_score            1     20.94 11773 2068.1
## - writing_score:reading_score             1     23.99 11776 2068.3
## - gender:parent_marital_status            3    110.86 11863 2068.6
## - parent_educ:lunch_type                  5    192.25 11944 2068.6
## - ethnic_group:reading_score              4    154.12 11906 2068.8
## - gender:writing_score                    1     35.92 11788 2068.9
## - ethnic_group:writing_score              4    159.49 11911 2069.0
## <none>                                                11752 2069.1
## - ethnic_group:parent_educ               20    829.83 12582 2069.3
## - parent_marital_status:practice_sport    5    206.09 11958 2069.3
## - practice_sport:reading_score            2    107.48 11859 2070.4
## - practice_sport:writing_score            2    109.03 11861 2070.5
## - is_first_child:wkly_study_hours         2    122.78 11874 2071.2
## - parent_educ:is_first_child              5    252.59 12004 2071.6
## - test_prep:parent_marital_status         3    173.51 11925 2071.7
## + transport_means:wkly_study_hours        2     19.87 11732 2072.1
## - lunch_type:practice_sport               2    146.03 11898 2072.3
## + gender:practice_sport                   2     10.92 11741 2072.5
## + practice_sport:transport_means          2     10.15 11742 2072.6
## - wkly_study_hours:reading_score          2    151.33 11903 2072.6
## + test_prep:practice_sport                2      7.07 11745 2072.7
## + gender:wkly_study_hours                 2      1.96 11750 2073.0
## + gender:ethnic_group                     4     76.90 11675 2073.2
## + ethnic_group:transport_means            4     65.98 11686 2073.7
## + practice_sport:wkly_study_hours         4     58.35 11693 2074.1
## - test_prep:transport_means               1    143.84 11896 2074.2
## + parent_marital_status:is_first_child    3     15.32 11736 2074.3
## + parent_marital_status:writing_score     3     12.39 11739 2074.4
## + parent_marital_status:reading_score     3     10.23 11742 2074.6
## + ethnic_group:lunch_type                 4     27.80 11724 2075.7
## - ethnic_group:is_first_child             4    298.14 12050 2075.8
## - lunch_type:is_first_child               1    220.68 11972 2078.0
## + gender:parent_educ                      5     15.88 11736 2078.3
## - is_first_child:transport_means          1    230.09 11982 2078.5
## + parent_educ:practice_sport             10    202.79 11549 2078.8
## + ethnic_group:practice_sport             8    117.05 11635 2079.2
## + parent_educ:wkly_study_hours           10    190.94 11561 2079.4
## + ethnic_group:parent_marital_status     11    211.77 11540 2080.3
## + ethnic_group:wkly_study_hours           8     88.57 11663 2080.6
## + parent_educ:parent_marital_status      15    247.77 11504 2086.5
## 
## Step:  AIC=2066.24
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:parent_marital_status + 
##     gender:is_first_child + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:wkly_study_hours  6    178.00 11993 2063.1
## - practice_sport:is_first_child           2     20.82 11836 2063.3
## - lunch_type:parent_marital_status        2     27.79 11843 2063.6
## - test_prep:wkly_study_hours              2     34.51 11850 2064.0
## - parent_educ:test_prep                   5    158.17 11973 2064.1
## - parent_educ:reading_score               5    159.13 11974 2064.1
## - gender:lunch_type                       1      0.01 11815 2064.2
## - lunch_type:reading_score                1      0.17 11815 2064.2
## - lunch_type:transport_means              1      0.47 11816 2064.3
## - lunch_type:writing_score                1      1.00 11816 2064.3
## - gender:transport_means                  1      1.70 11817 2064.3
## - transport_means:reading_score           1      2.65 11818 2064.4
## - test_prep:writing_score                 1      2.69 11818 2064.4
## - is_first_child:writing_score            1      3.48 11819 2064.4
## - gender:reading_score                    1      3.50 11819 2064.4
## - gender:test_prep                        1      4.05 11819 2064.4
## - transport_means:writing_score           1      4.48 11820 2064.5
## - test_prep:reading_score                 1      4.73 11820 2064.5
## - parent_educ:transport_means             5    167.77 11983 2064.6
## - gender:is_first_child                   1      6.60 11822 2064.6
## - lunch_type:test_prep                    1      6.84 11822 2064.6
## - test_prep:is_first_child                1      7.35 11822 2064.6
## - ethnic_group:test_prep                  4    130.46 11946 2064.7
## - gender:parent_marital_status            3     95.61 11911 2065.0
## - wkly_study_hours:writing_score          2     58.54 11874 2065.2
## - parent_educ:writing_score               5    179.92 11995 2065.2
## - is_first_child:reading_score            1     19.04 11834 2065.2
## - writing_score:reading_score             1     20.67 11836 2065.3
## - lunch_type:wkly_study_hours             2     61.21 11876 2065.3
## - parent_educ:lunch_type                  5    192.04 12007 2065.8
## - gender:writing_score                    1     37.56 11853 2066.1
## - ethnic_group:parent_educ               20    826.96 12642 2066.2
## <none>                                                11815 2066.2
## - ethnic_group:reading_score              4    165.36 11980 2066.4
## - ethnic_group:writing_score              4    165.87 11981 2066.5
## - test_prep:parent_marital_status         3    147.80 11963 2067.6
## - practice_sport:reading_score            2    108.84 11924 2067.7
## - practice_sport:writing_score            2    112.54 11928 2067.8
## - is_first_child:wkly_study_hours         2    117.82 11933 2068.1
## - parent_marital_status:practice_sport    5    249.71 12065 2068.6
## + parent_marital_status:transport_means   3     63.35 11752 2069.1
## + transport_means:wkly_study_hours        2     19.02 11796 2069.3
## + gender:practice_sport                   2     17.46 11798 2069.4
## - lunch_type:practice_sport               2    147.90 11963 2069.6
## + practice_sport:transport_means          2     12.06 11803 2069.6
## - parent_educ:is_first_child              5    271.87 12087 2069.7
## - wkly_study_hours:reading_score          2    154.57 11970 2069.9
## + test_prep:practice_sport                2      4.97 11810 2070.0
## + gender:ethnic_group                     4     83.31 11732 2070.1
## + gender:wkly_study_hours                 2      1.81 11813 2070.2
## + parent_marital_status:is_first_child    3     26.64 11788 2070.9
## - test_prep:transport_means               1    141.25 11956 2071.2
## + ethnic_group:transport_means            4     56.78 11758 2071.4
## + parent_marital_status:writing_score     3      8.42 11807 2071.8
## + parent_marital_status:reading_score     3      6.98 11808 2071.9
## + practice_sport:wkly_study_hours         4     40.16 11775 2072.2
## + ethnic_group:lunch_type                 4     30.28 11785 2072.7
## - ethnic_group:is_first_child             4    305.40 12120 2073.3
## - is_first_child:transport_means          1    221.80 12037 2075.2
## - lunch_type:is_first_child               1    224.54 12040 2075.3
## + gender:parent_educ                      5     13.02 11802 2075.6
## + parent_educ:practice_sport             10    199.93 11615 2076.2
## + ethnic_group:practice_sport             8    111.76 11703 2076.6
## + ethnic_group:wkly_study_hours           8    103.36 11712 2077.1
## + parent_educ:wkly_study_hours           10    168.22 11647 2077.8
## + ethnic_group:parent_marital_status     11    196.07 11619 2078.4
## + parent_educ:parent_marital_status      15    236.82 11578 2084.3
## 
## Step:  AIC=2063.06
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:parent_marital_status + 
##     gender:is_first_child + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_marital_status            3     47.01 12040 2059.4
## - practice_sport:is_first_child           2     14.75 12008 2059.8
## - ethnic_group:parent_educ               20    777.17 12770 2060.1
## - lunch_type:parent_marital_status        2     23.19 12016 2060.2
## - parent_educ:reading_score               5    150.98 12144 2060.4
## - test_prep:wkly_study_hours              2     31.89 12025 2060.6
## - lunch_type:transport_means              1      0.07 11993 2061.1
## - lunch_type:reading_score                1      0.68 11994 2061.1
## - transport_means:reading_score           1      0.89 11994 2061.1
## - gender:transport_means                  1      1.00 11994 2061.1
## - gender:test_prep                        1      1.48 11995 2061.1
## - lunch_type:test_prep                    1      1.53 11995 2061.1
## - gender:reading_score                    1      1.63 11995 2061.1
## - gender:lunch_type                       1      1.73 11995 2061.1
## - lunch_type:writing_score                1      2.14 11995 2061.2
## - gender:is_first_child                   1      2.37 11996 2061.2
## - test_prep:writing_score                 1      2.77 11996 2061.2
## - is_first_child:writing_score            1      3.88 11997 2061.2
## - test_prep:reading_score                 1      4.46 11998 2061.3
## - parent_educ:lunch_type                  5    168.57 12162 2061.3
## - ethnic_group:test_prep                  4    127.78 12121 2061.3
## - parent_educ:test_prep                   5    168.99 12162 2061.3
## - test_prep:is_first_child                1      5.32 11998 2061.3
## - parent_educ:writing_score               5    169.54 12163 2061.3
## - transport_means:writing_score           1      7.71 12001 2061.4
## - wkly_study_hours:writing_score          2     49.08 12042 2061.5
## - lunch_type:wkly_study_hours             2     54.20 12047 2061.7
## - is_first_child:reading_score            1     21.65 12015 2062.1
## - writing_score:reading_score             1     23.68 12017 2062.2
## - parent_educ:transport_means             5    191.53 12185 2062.4
## - gender:writing_score                    1     31.63 12025 2062.6
## <none>                                                11993 2063.1
## - test_prep:parent_marital_status         3    152.72 12146 2064.5
## - practice_sport:reading_score            2    118.66 12112 2064.9
## - practice_sport:writing_score            2    126.77 12120 2065.3
## - ethnic_group:reading_score              4    211.20 12204 2065.4
## - wkly_study_hours:reading_score          2    131.56 12125 2065.5
## - ethnic_group:writing_score              4    215.37 12208 2065.6
## - lunch_type:practice_sport               2    133.40 12126 2065.6
## + gender:practice_sport                   2     24.04 11969 2065.9
## - parent_marital_status:practice_sport    5    269.16 12262 2066.2
## + parent_marital_status:wkly_study_hours  6    178.00 11815 2066.2
## + transport_means:wkly_study_hours        2     15.92 11977 2066.3
## - parent_educ:is_first_child              5    272.33 12265 2066.3
## + practice_sport:transport_means          2     10.68 11982 2066.5
## + gender:wkly_study_hours                 2      9.46 11984 2066.6
## + test_prep:practice_sport                2      5.03 11988 2066.8
## + gender:ethnic_group                     4     83.41 11910 2066.9
## - is_first_child:wkly_study_hours         2    163.08 12156 2067.0
## + parent_marital_status:transport_means   3     36.28 11957 2067.3
## + parent_marital_status:writing_score     3     23.50 11970 2067.9
## + parent_marital_status:is_first_child    3     20.56 11972 2068.1
## - test_prep:transport_means               1    146.49 12140 2068.2
## + parent_marital_status:reading_score     3     16.62 11976 2068.2
## + ethnic_group:transport_means            4     45.38 11948 2068.8
## + practice_sport:wkly_study_hours         4     31.67 11961 2069.5
## - ethnic_group:is_first_child             4    304.17 12297 2069.8
## + ethnic_group:lunch_type                 4     22.84 11970 2069.9
## - lunch_type:is_first_child               1    210.47 12204 2071.3
## + parent_educ:practice_sport             10    218.59 11774 2072.2
## + gender:parent_educ                      5      8.50 11985 2072.6
## + ethnic_group:parent_marital_status     11    249.36 11744 2072.7
## + ethnic_group:practice_sport             8    114.27 11879 2073.4
## + parent_educ:wkly_study_hours           10    179.28 11814 2074.2
## + ethnic_group:wkly_study_hours           8     95.91 11897 2074.3
## - is_first_child:transport_means          1    285.88 12279 2075.0
## + parent_educ:parent_marital_status      15    243.78 11749 2080.9
## 
## Step:  AIC=2059.37
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:parent_educ + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     ethnic_group:writing_score + ethnic_group:reading_score + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_educ               20    761.88 12802 2055.6
## - practice_sport:is_first_child           2     19.20 12059 2056.3
## - parent_educ:reading_score               5    150.49 12191 2056.7
## - lunch_type:parent_marital_status        2     28.00 12068 2056.7
## - ethnic_group:test_prep                  4    116.40 12156 2057.0
## - test_prep:wkly_study_hours              2     34.93 12075 2057.1
## - parent_educ:test_prep                   5    158.45 12199 2057.1
## - parent_educ:lunch_type                  5    162.89 12203 2057.3
## - lunch_type:transport_means              1      0.03 12040 2057.4
## - transport_means:reading_score           1      0.13 12040 2057.4
## - gender:reading_score                    1      0.70 12041 2057.4
## - lunch_type:reading_score                1      0.76 12041 2057.4
## - gender:transport_means                  1      0.79 12041 2057.4
## - gender:lunch_type                       1      1.07 12041 2057.4
## - gender:test_prep                        1      1.34 12041 2057.4
## - lunch_type:writing_score                1      1.96 12042 2057.5
## - gender:is_first_child                   1      2.71 12043 2057.5
## - lunch_type:test_prep                    1      2.80 12043 2057.5
## - test_prep:writing_score                 1      4.04 12044 2057.6
## - is_first_child:writing_score            1      4.09 12044 2057.6
## - parent_educ:writing_score               5    169.04 12209 2057.6
## - test_prep:is_first_child                1      4.88 12045 2057.6
## - test_prep:reading_score                 1      7.16 12047 2057.7
## - wkly_study_hours:writing_score          2     49.59 12090 2057.8
## - transport_means:writing_score           1     11.03 12051 2057.9
## - lunch_type:wkly_study_hours             2     57.38 12098 2058.2
## - writing_score:reading_score             1     21.16 12061 2058.4
## - is_first_child:reading_score            1     22.05 12062 2058.4
## - gender:writing_score                    1     26.64 12067 2058.7
## - parent_educ:transport_means             5    199.12 12239 2059.0
## <none>                                                12040 2059.4
## - practice_sport:reading_score            2    115.83 12156 2061.0
## - test_prep:parent_marital_status         3    160.84 12201 2061.2
## - practice_sport:writing_score            2    124.74 12165 2061.4
## - wkly_study_hours:reading_score          2    128.76 12169 2061.6
## - lunch_type:practice_sport               2    129.02 12169 2061.7
## - ethnic_group:reading_score              4    216.36 12256 2061.9
## - parent_marital_status:practice_sport    5    258.54 12299 2061.9
## - ethnic_group:writing_score              4    218.56 12259 2062.0
## + gender:practice_sport                   2     23.24 12017 2062.2
## + transport_means:wkly_study_hours        2     20.32 12020 2062.4
## - parent_educ:is_first_child              5    275.56 12316 2062.7
## + gender:wkly_study_hours                 2     11.79 12028 2062.8
## + practice_sport:transport_means          2      8.42 12032 2062.9
## + gender:ethnic_group                     4     87.91 11952 2063.0
## + test_prep:practice_sport                2      6.47 12034 2063.1
## + gender:parent_marital_status            3     47.01 11993 2063.1
## + parent_marital_status:is_first_child    3     43.60 11996 2063.2
## + parent_marital_status:transport_means   3     37.95 12002 2063.5
## - is_first_child:wkly_study_hours         2    170.54 12211 2063.7
## - test_prep:transport_means               1    149.93 12190 2064.7
## + parent_marital_status:writing_score     3     12.28 12028 2064.8
## + parent_marital_status:reading_score     3      9.60 12030 2064.9
## + parent_marital_status:wkly_study_hours  6    129.39 11911 2065.0
## + ethnic_group:transport_means            4     47.82 11992 2065.0
## + practice_sport:wkly_study_hours         4     38.07 12002 2065.5
## - ethnic_group:is_first_child             4    303.95 12344 2066.1
## + ethnic_group:lunch_type                 4     23.44 12017 2066.2
## + ethnic_group:parent_marital_status     11    291.26 11749 2066.9
## - lunch_type:is_first_child               1    214.71 12255 2067.8
## + gender:parent_educ                      5      6.46 12034 2069.1
## + parent_educ:practice_sport             10    202.74 11837 2069.3
## + ethnic_group:practice_sport             8    118.40 11922 2069.5
## + parent_educ:wkly_study_hours           10    177.47 11863 2070.6
## + ethnic_group:wkly_study_hours           8     84.98 11955 2071.2
## - is_first_child:transport_means          1    296.04 12336 2071.7
## + parent_educ:parent_marital_status      15    250.25 11790 2077.0
## 
## Step:  AIC=2055.57
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:reading_score               5     99.29 12901 2050.1
## - parent_educ:writing_score               5    121.86 12924 2051.2
## - parent_educ:lunch_type                  5    154.92 12957 2052.7
## - practice_sport:is_first_child           2     40.83 12843 2053.4
## - lunch_type:parent_marital_status        2     41.58 12844 2053.5
## - lunch_type:test_prep                    1      0.19 12802 2053.6
## - gender:is_first_child                   1      0.28 12802 2053.6
## - gender:transport_means                  1      0.50 12802 2053.6
## - lunch_type:transport_means              1      0.56 12802 2053.6
## - gender:reading_score                    1      0.64 12803 2053.6
## - gender:lunch_type                       1      0.75 12803 2053.6
## - is_first_child:reading_score            1      0.80 12803 2053.6
## - transport_means:reading_score           1      0.85 12803 2053.6
## - test_prep:writing_score                 1      3.12 12805 2053.7
## - is_first_child:writing_score            1      3.26 12805 2053.7
## - test_prep:is_first_child                1      3.46 12805 2053.7
## - test_prep:wkly_study_hours              2     48.35 12850 2053.8
## - lunch_type:reading_score                1      5.45 12807 2053.8
## - lunch_type:writing_score                1      6.37 12808 2053.9
## - test_prep:reading_score                 1      7.70 12810 2053.9
## - wkly_study_hours:writing_score          2     51.61 12854 2053.9
## - transport_means:writing_score           1      9.25 12811 2054.0
## - gender:test_prep                        1     10.75 12813 2054.1
## - writing_score:reading_score             1     11.51 12814 2054.1
## - parent_educ:test_prep                   5    193.00 12995 2054.4
## - gender:writing_score                    1     24.39 12826 2054.7
## - ethnic_group:test_prep                  4    157.08 12959 2054.8
## - ethnic_group:reading_score              4    158.29 12960 2054.8
## - ethnic_group:writing_score              4    163.74 12966 2055.1
## - lunch_type:wkly_study_hours             2     80.06 12882 2055.2
## <none>                                                12802 2055.6
## - lunch_type:practice_sport               2     93.02 12895 2055.8
## - parent_educ:transport_means             5    227.14 13029 2055.9
## - test_prep:parent_marital_status         3    153.38 12955 2056.6
## - parent_marital_status:practice_sport    5    245.91 13048 2056.8
## + practice_sport:transport_means          2     45.02 12757 2057.5
## + gender:ethnic_group                     4    126.01 12676 2057.7
## - wkly_study_hours:reading_score          2    138.39 12940 2057.9
## - parent_educ:is_first_child              5    277.92 13080 2058.2
## + gender:practice_sport                   2     22.49 12780 2058.5
## + gender:wkly_study_hours                 2     20.55 12781 2058.6
## - practice_sport:reading_score            2    158.02 12960 2058.8
## - practice_sport:writing_score            2    163.45 12965 2059.1
## + test_prep:practice_sport                2     11.00 12791 2059.1
## + transport_means:wkly_study_hours        2     10.37 12792 2059.1
## + ethnic_group:parent_educ               20    761.88 12040 2059.4
## - test_prep:transport_means               1    133.98 12936 2059.7
## + parent_marital_status:transport_means   3     38.78 12763 2059.8
## - ethnic_group:is_first_child             4    272.11 13074 2060.0
## + gender:parent_marital_status            3     31.72 12770 2060.1
## + parent_marital_status:is_first_child    3     28.07 12774 2060.3
## - is_first_child:wkly_study_hours         2    201.32 13003 2060.8
## + ethnic_group:lunch_type                 4     57.78 12744 2060.9
## - lunch_type:is_first_child               1    162.17 12964 2061.0
## + ethnic_group:transport_means            4     50.62 12751 2061.2
## + parent_marital_status:writing_score     3      4.10 12798 2061.4
## + parent_marital_status:reading_score     3      3.55 12798 2061.4
## + practice_sport:wkly_study_hours         4     10.27 12792 2063.1
## + ethnic_group:parent_marital_status     11    308.30 12494 2063.2
## + parent_marital_status:wkly_study_hours  6     91.87 12710 2063.3
## + ethnic_group:practice_sport             8    171.92 12630 2063.6
## + gender:parent_educ                      5     26.78 12775 2064.3
## + parent_educ:practice_sport             10    194.28 12608 2066.5
## - is_first_child:transport_means          1    301.30 13103 2067.3
## + ethnic_group:wkly_study_hours           8     80.42 12722 2067.8
## + parent_educ:wkly_study_hours           10    161.83 12640 2068.1
## + parent_educ:parent_marital_status      15    307.27 12495 2071.2
## 
## Step:  AIC=2050.13
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:writing_score               5    132.93 13034 2046.2
## - parent_educ:lunch_type                  5    144.54 13046 2046.7
## - lunch_type:parent_marital_status        2     43.17 12944 2048.1
## - gender:reading_score                    1      0.02 12901 2048.1
## - gender:is_first_child                   1      0.02 12901 2048.1
## - lunch_type:test_prep                    1      0.06 12901 2048.1
## - transport_means:reading_score           1      0.25 12902 2048.1
## - gender:lunch_type                       1      0.30 12902 2048.1
## - is_first_child:writing_score            1      1.35 12903 2048.2
## - lunch_type:transport_means              1      1.48 12903 2048.2
## - gender:transport_means                  1      1.74 12903 2048.2
## - is_first_child:reading_score            1      2.51 12904 2048.2
## - parent_educ:test_prep                   5    178.73 13080 2048.2
## - wkly_study_hours:writing_score          2     47.43 12949 2048.3
## - practice_sport:is_first_child           2     47.87 12949 2048.3
## - test_prep:writing_score                 1      4.52 12906 2048.3
## - lunch_type:writing_score                1      5.11 12906 2048.4
## - lunch_type:reading_score                1      5.23 12906 2048.4
## - test_prep:is_first_child                1      5.82 12907 2048.4
## - gender:test_prep                        1      9.38 12911 2048.6
## - test_prep:wkly_study_hours              2     54.22 12956 2048.6
## - writing_score:reading_score             1     10.62 12912 2048.6
## - test_prep:reading_score                 1     11.24 12912 2048.6
## - transport_means:writing_score           1     12.87 12914 2048.7
## - ethnic_group:reading_score              4    147.16 13048 2048.8
## - ethnic_group:test_prep                  4    147.50 13049 2048.8
## - ethnic_group:writing_score              4    149.16 13050 2048.9
## - gender:writing_score                    1     18.32 12920 2049.0
## <none>                                                12901 2050.1
## - lunch_type:wkly_study_hours             2     88.07 12989 2050.1
## - lunch_type:practice_sport               2     88.33 12990 2050.2
## - parent_marital_status:practice_sport    5    231.06 13132 2050.6
## - parent_educ:transport_means             5    232.96 13134 2050.7
## - test_prep:parent_marital_status         3    153.48 13055 2051.1
## - wkly_study_hours:reading_score          2    128.65 13030 2052.0
## + practice_sport:transport_means          2     36.08 12865 2052.5
## + gender:wkly_study_hours                 2     22.07 12879 2053.1
## + gender:ethnic_group                     4    107.56 12794 2053.2
## + gender:practice_sport                   2     18.23 12883 2053.3
## + transport_means:wkly_study_hours        2      9.21 12892 2053.7
## + test_prep:practice_sport                2      8.02 12893 2053.8
## - practice_sport:writing_score            2    175.39 13077 2054.1
## - practice_sport:reading_score            2    177.29 13079 2054.2
## - ethnic_group:is_first_child             4    268.16 13169 2054.3
## + parent_marital_status:transport_means   3     36.54 12865 2054.4
## - test_prep:transport_means               1    140.19 13042 2054.5
## + gender:parent_marital_status            3     32.21 12869 2054.7
## + parent_marital_status:is_first_child    3     25.26 12876 2055.0
## - parent_educ:is_first_child              5    338.63 13240 2055.4
## + ethnic_group:lunch_type                 4     57.08 12844 2055.5
## - lunch_type:is_first_child               1    163.21 13064 2055.5
## + parent_educ:reading_score               5     99.29 12802 2055.6
## - is_first_child:wkly_study_hours         2    209.25 13110 2055.6
## + parent_marital_status:reading_score     3      5.31 12896 2055.9
## + parent_marital_status:writing_score     3      4.53 12897 2055.9
## + ethnic_group:transport_means            4     45.84 12855 2056.0
## + ethnic_group:parent_educ               20    710.68 12191 2056.7
## + parent_marital_status:wkly_study_hours  6     94.01 12807 2057.8
## + practice_sport:wkly_study_hours         4      4.76 12896 2057.9
## + ethnic_group:parent_marital_status     11    291.03 12610 2058.7
## + ethnic_group:practice_sport             8    159.66 12742 2058.8
## + gender:parent_educ                      5     17.54 12884 2059.3
## + parent_educ:practice_sport             10    198.47 12703 2061.0
## - is_first_child:transport_means          1    305.26 13206 2061.9
## + parent_educ:wkly_study_hours           10    161.81 12740 2062.7
## + ethnic_group:wkly_study_hours           8     71.42 12830 2062.8
## + parent_educ:parent_marital_status      15    291.89 12609 2066.6
## 
## Step:  AIC=2046.17
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:lunch_type                  5    149.37 13184 2042.9
## - lunch_type:parent_marital_status        2     37.45 13072 2043.9
## - ethnic_group:reading_score              4    129.34 13164 2044.0
## - parent_educ:test_prep                   5    174.12 13208 2044.0
## - ethnic_group:writing_score              4    132.21 13166 2044.1
## - lunch_type:test_prep                    1      0.00 13034 2044.2
## - gender:reading_score                    1      0.11 13034 2044.2
## - gender:is_first_child                   1      0.12 13034 2044.2
## - gender:lunch_type                       1      0.28 13034 2044.2
## - lunch_type:transport_means              1      0.59 13035 2044.2
## - practice_sport:is_first_child           2     45.12 13079 2044.2
## - is_first_child:writing_score            1      1.23 13035 2044.2
## - test_prep:writing_score                 1      1.25 13036 2044.2
## - is_first_child:reading_score            1      1.37 13036 2044.2
## - gender:transport_means                  1      1.61 13036 2044.2
## - transport_means:reading_score           1      1.99 13036 2044.3
## - lunch_type:reading_score                1      2.53 13037 2044.3
## - lunch_type:writing_score                1      2.83 13037 2044.3
## - test_prep:reading_score                 1      4.94 13039 2044.4
## - test_prep:wkly_study_hours              2     50.51 13085 2044.5
## - transport_means:writing_score           1      6.37 13041 2044.5
## - test_prep:is_first_child                1      8.15 13042 2044.5
## - gender:test_prep                        1      8.99 13043 2044.6
## - wkly_study_hours:writing_score          2     57.10 13091 2044.8
## - gender:writing_score                    1     13.28 13048 2044.8
## - ethnic_group:test_prep                  4    153.20 13187 2045.1
## - writing_score:reading_score             1     32.85 13067 2045.7
## - lunch_type:wkly_study_hours             2     86.60 13121 2046.1
## <none>                                                13034 2046.2
## - parent_educ:transport_means             5    227.22 13261 2046.4
## - lunch_type:practice_sport               2     98.79 13133 2046.6
## - parent_marital_status:practice_sport    5    233.78 13268 2046.7
## - test_prep:parent_marital_status         3    165.30 13200 2047.6
## + practice_sport:transport_means          2     44.11 12990 2048.2
## - wkly_study_hours:reading_score          2    148.86 13183 2048.9
## + gender:wkly_study_hours                 2     24.32 13010 2049.1
## + gender:ethnic_group                     4    107.46 12927 2049.3
## + gender:practice_sport                   2     13.88 13020 2049.5
## + transport_means:wkly_study_hours        2     11.98 13022 2049.6
## + test_prep:practice_sport                2      7.52 13027 2049.8
## - test_prep:transport_means               1    126.19 13160 2049.9
## + parent_educ:writing_score               5    132.93 12901 2050.1
## + parent_marital_status:transport_means   3     41.71 12992 2050.3
## - ethnic_group:is_first_child             4    275.08 13309 2050.5
## + gender:parent_marital_status            3     34.76 12999 2050.6
## - practice_sport:reading_score            2    194.03 13228 2050.9
## - practice_sport:writing_score            2    194.79 13229 2050.9
## + parent_marital_status:is_first_child    3     24.10 13010 2051.1
## + parent_educ:reading_score               5    110.35 12924 2051.2
## + ethnic_group:lunch_type                 4     62.92 12971 2051.3
## - parent_educ:is_first_child              5    350.50 13385 2051.8
## - is_first_child:wkly_study_hours         2    217.55 13252 2051.9
## + parent_marital_status:writing_score     3      3.61 13031 2052.0
## + parent_marital_status:reading_score     3      2.81 13031 2052.1
## + ethnic_group:transport_means            4     42.26 12992 2052.3
## + ethnic_group:parent_educ               20    705.65 12328 2053.3
## - lunch_type:is_first_child               1    215.45 13250 2053.8
## + gender:parent_educ                      5     48.26 12986 2054.0
## + practice_sport:wkly_study_hours         4      2.30 13032 2054.1
## + parent_marital_status:wkly_study_hours  6     82.07 12952 2054.4
## + ethnic_group:practice_sport             8    167.80 12866 2054.5
## + ethnic_group:parent_marital_status     11    281.37 12753 2055.3
## - is_first_child:transport_means          1    299.22 13333 2057.6
## + parent_educ:practice_sport             10    178.84 12855 2058.0
## + ethnic_group:wkly_study_hours           8     76.15 12958 2058.7
## + parent_educ:wkly_study_hours           10    152.18 12882 2059.2
## + parent_educ:parent_marital_status      15    332.73 12702 2060.9
## 
## Step:  AIC=2042.9
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score + 
##     ethnic_group:reading_score + parent_educ:test_prep + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:reading_score              4    110.19 13294 2039.8
## - ethnic_group:writing_score              4    117.20 13301 2040.1
## - practice_sport:is_first_child           2     41.58 13225 2040.8
## - lunch_type:parent_marital_status        2     43.90 13228 2040.9
## - gender:is_first_child                   1      0.00 13184 2040.9
## - is_first_child:reading_score            1      0.09 13184 2040.9
## - transport_means:reading_score           1      0.14 13184 2040.9
## - lunch_type:test_prep                    1      0.16 13184 2040.9
## - gender:reading_score                    1      0.16 13184 2040.9
## - gender:lunch_type                       1      0.81 13184 2040.9
## - lunch_type:writing_score                1      0.92 13184 2040.9
## - lunch_type:reading_score                1      1.36 13185 2041.0
## - test_prep:writing_score                 1      2.01 13186 2041.0
## - lunch_type:transport_means              1      3.17 13187 2041.0
## - test_prep:wkly_study_hours              2     48.09 13232 2041.0
## - is_first_child:writing_score            1      3.49 13187 2041.0
## - parent_educ:test_prep                   5    183.90 13368 2041.1
## - gender:test_prep                        1      5.19 13189 2041.1
## - test_prep:reading_score                 1      5.50 13189 2041.1
## - gender:transport_means                  1      5.73 13189 2041.2
## - wkly_study_hours:writing_score          2     51.56 13235 2041.2
## - test_prep:is_first_child                1      6.82 13190 2041.2
## - transport_means:writing_score           1     11.36 13195 2041.4
## - gender:writing_score                    1     18.03 13202 2041.7
## - writing_score:reading_score             1     32.07 13216 2042.3
## - lunch_type:practice_sport               2     84.09 13268 2042.7
## - ethnic_group:test_prep                  4    174.68 13358 2042.7
## <none>                                                13184 2042.9
## - parent_educ:transport_means             5    229.86 13413 2043.1
## - lunch_type:wkly_study_hours             2     97.27 13281 2043.2
## - test_prep:parent_marital_status         3    162.56 13346 2044.1
## - parent_marital_status:practice_sport    5    259.71 13443 2044.4
## + practice_sport:transport_means          2     46.36 13137 2044.8
## - wkly_study_hours:reading_score          2    135.42 13319 2044.9
## + transport_means:wkly_study_hours        2     20.65 13163 2046.0
## + gender:wkly_study_hours                 2     17.75 13166 2046.1
## + gender:ethnic_group                     4    106.45 13077 2046.1
## + parent_educ:lunch_type                  5    149.37 13034 2046.2
## + gender:practice_sport                   2     12.74 13171 2046.3
## + test_prep:practice_sport                2     12.20 13171 2046.3
## + parent_educ:writing_score               5    137.76 13046 2046.7
## + parent_educ:reading_score               5    134.53 13049 2046.8
## - parent_educ:is_first_child              5    316.22 13500 2046.9
## + parent_marital_status:transport_means   3     41.45 13142 2047.0
## + gender:parent_marital_status            3     31.51 13152 2047.5
## - test_prep:transport_means               1    149.86 13333 2047.6
## - ethnic_group:is_first_child             4    286.27 13470 2047.6
## - practice_sport:reading_score            2    197.75 13381 2047.7
## + ethnic_group:lunch_type                 4     68.75 13115 2047.8
## - practice_sport:writing_score            2    202.65 13386 2047.9
## + parent_marital_status:is_first_child    3     18.93 13165 2048.1
## + parent_marital_status:writing_score     3      7.74 13176 2048.6
## + parent_marital_status:reading_score     3      7.34 13176 2048.6
## + ethnic_group:transport_means            4     49.95 13134 2048.7
## - is_first_child:wkly_study_hours         2    236.87 13420 2049.4
## - lunch_type:is_first_child               1    202.51 13386 2049.9
## + practice_sport:wkly_study_hours         4      2.96 13181 2050.8
## + gender:parent_educ                      5     47.07 13136 2050.8
## + ethnic_group:practice_sport             8    175.74 13008 2051.0
## + ethnic_group:parent_educ               20    691.00 12493 2051.1
## + parent_marital_status:wkly_study_hours  6     62.37 13121 2052.1
## + ethnic_group:parent_marital_status     11    261.69 12922 2053.1
## + parent_educ:practice_sport             10    183.88 13000 2054.6
## - is_first_child:transport_means          1    313.26 13497 2054.8
## + ethnic_group:wkly_study_hours           8     81.47 13102 2055.2
## + parent_educ:wkly_study_hours           10    131.72 13052 2057.0
## + parent_educ:parent_marital_status      15    311.73 12872 2058.8
## 
## Step:  AIC=2039.81
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:writing_score              4     35.77 13330 2033.4
## - practice_sport:is_first_child           2     35.34 13329 2037.4
## - lunch_type:test_prep                    1      0.00 13294 2037.8
## - gender:is_first_child                   1      0.10 13294 2037.8
## - transport_means:reading_score           1      0.25 13294 2037.8
## - lunch_type:writing_score                1      0.26 13294 2037.8
## - lunch_type:reading_score                1      0.57 13294 2037.8
## - test_prep:writing_score                 1      1.03 13295 2037.8
## - gender:lunch_type                       1      1.27 13295 2037.9
## - is_first_child:reading_score            1      2.22 13296 2037.9
## - lunch_type:parent_marital_status        2     47.44 13341 2037.9
## - test_prep:reading_score                 1      2.81 13297 2037.9
## - gender:transport_means                  1      3.10 13297 2038.0
## - lunch_type:transport_means              1      3.27 13297 2038.0
## - test_prep:is_first_child                1      4.05 13298 2038.0
## - test_prep:wkly_study_hours              2     50.60 13344 2038.0
## - parent_educ:test_prep                   5    187.46 13481 2038.1
## - gender:reading_score                    1      8.85 13303 2038.2
## - gender:test_prep                        1      9.34 13303 2038.2
## - transport_means:writing_score           1     10.35 13304 2038.3
## - is_first_child:writing_score            1     12.70 13306 2038.4
## - wkly_study_hours:writing_score          2     60.65 13354 2038.5
## - lunch_type:practice_sport               2     74.40 13368 2039.1
## - lunch_type:wkly_study_hours             2     78.66 13372 2039.3
## - writing_score:reading_score             1     38.42 13332 2039.5
## - gender:writing_score                    1     43.10 13337 2039.7
## <none>                                                13294 2039.8
## - ethnic_group:test_prep                  4    194.01 13488 2040.4
## - parent_educ:transport_means             5    245.55 13539 2040.6
## - test_prep:parent_marital_status         3    163.85 13458 2041.0
## - parent_marital_status:practice_sport    5    257.66 13551 2041.1
## + practice_sport:transport_means          2     46.29 13248 2041.8
## - wkly_study_hours:reading_score          2    149.05 13443 2042.4
## + ethnic_group:reading_score              4    110.19 13184 2042.9
## + gender:wkly_study_hours                 2     17.62 13276 2043.0
## + transport_means:wkly_study_hours        2     13.21 13281 2043.2
## + gender:practice_sport                   2     10.93 13283 2043.3
## - parent_educ:is_first_child              5    311.51 13605 2043.5
## + test_prep:practice_sport                2      6.99 13287 2043.5
## + parent_marital_status:transport_means   3     50.67 13243 2043.5
## - test_prep:transport_means               1    130.38 13424 2043.6
## + parent_educ:lunch_type                  5    130.22 13164 2044.0
## + gender:ethnic_group                     4     83.01 13211 2044.1
## + parent_educ:writing_score               5    126.11 13168 2044.2
## + gender:parent_marital_status            3     33.43 13260 2044.3
## + parent_educ:reading_score               5    119.35 13174 2044.5
## + ethnic_group:lunch_type                 4     74.27 13220 2044.5
## + parent_marital_status:is_first_child    3     19.54 13274 2044.9
## + parent_marital_status:writing_score     3     14.08 13280 2045.2
## - is_first_child:wkly_study_hours         2    214.25 13508 2045.2
## - ethnic_group:is_first_child             4    307.90 13602 2045.3
## + parent_marital_status:reading_score     3     10.29 13284 2045.3
## + ethnic_group:transport_means            4     50.91 13243 2045.5
## - practice_sport:writing_score            2    222.36 13516 2045.6
## - practice_sport:reading_score            2    222.71 13516 2045.6
## - lunch_type:is_first_child               1    210.80 13505 2047.1
## + gender:parent_educ                      5     49.54 13244 2047.6
## + practice_sport:wkly_study_hours         4      1.97 13292 2047.7
## + parent_marital_status:wkly_study_hours  6     85.61 13208 2048.0
## + ethnic_group:practice_sport             8    148.00 13146 2049.2
## + ethnic_group:parent_educ               20    651.69 12642 2050.2
## + ethnic_group:parent_marital_status     11    252.26 13042 2050.5
## - is_first_child:transport_means          1    310.96 13605 2051.4
## + parent_educ:practice_sport             10    177.52 13116 2051.9
## + ethnic_group:wkly_study_hours           8     70.38 13223 2052.7
## + parent_educ:wkly_study_hours           10    149.49 13144 2053.1
## + parent_educ:parent_marital_status      15    305.22 12988 2056.1
## 
## Step:  AIC=2033.39
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     transport_means:reading_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:is_first_child           2     34.43 13364 2030.9
## - lunch_type:test_prep                    1      0.02 13330 2031.4
## - lunch_type:writing_score                1      0.02 13330 2031.4
## - lunch_type:reading_score                1      0.10 13330 2031.4
## - transport_means:reading_score           1      0.27 13330 2031.4
## - gender:is_first_child                   1      0.36 13330 2031.4
## - parent_educ:test_prep                   5    182.37 13512 2031.4
## - gender:lunch_type                       1      0.41 13330 2031.4
## - is_first_child:reading_score            1      0.86 13330 2031.4
## - test_prep:writing_score                 1      1.16 13331 2031.4
## - lunch_type:parent_marital_status        2     47.31 13377 2031.5
## - test_prep:reading_score                 1      2.38 13332 2031.5
## - gender:transport_means                  1      2.83 13332 2031.5
## - lunch_type:transport_means              1      4.29 13334 2031.6
## - test_prep:is_first_child                1      5.38 13335 2031.6
## - test_prep:wkly_study_hours              2     52.10 13382 2031.7
## - is_first_child:writing_score            1      8.99 13338 2031.8
## - gender:reading_score                    1      9.57 13339 2031.8
## - transport_means:writing_score           1     10.71 13340 2031.9
## - gender:test_prep                        1     12.74 13342 2032.0
## - wkly_study_hours:writing_score          2     64.66 13394 2032.2
## - lunch_type:practice_sport               2     68.01 13398 2032.4
## - lunch_type:wkly_study_hours             2     87.17 13417 2033.2
## - ethnic_group:test_prep                  4    180.69 13510 2033.3
## - writing_score:reading_score             1     44.61 13374 2033.4
## <none>                                                13330 2033.4
## - gender:writing_score                    1     47.67 13377 2033.5
## - test_prep:parent_marital_status         3    153.56 13483 2034.2
## - parent_educ:transport_means             5    254.65 13584 2034.6
## - parent_marital_status:practice_sport    5    265.85 13595 2035.0
## + practice_sport:transport_means          2     43.34 13286 2035.5
## - wkly_study_hours:reading_score          2    149.95 13480 2036.0
## + gender:wkly_study_hours                 2     19.75 13310 2036.5
## + transport_means:wkly_study_hours        2     14.37 13315 2036.8
## + gender:practice_sport                   2     12.75 13317 2036.8
## - parent_educ:is_first_child              5    308.70 13638 2036.9
## + test_prep:practice_sport                2      7.10 13322 2037.1
## + parent_marital_status:transport_means   3     43.84 13286 2037.5
## + parent_educ:lunch_type                  5    132.91 13197 2037.5
## - test_prep:transport_means               1    145.18 13475 2037.8
## + gender:ethnic_group                     4     77.82 13252 2037.9
## + gender:parent_marital_status            3     32.63 13297 2038.0
## + parent_educ:writing_score               5    118.16 13211 2038.1
## + parent_educ:reading_score               5    113.69 13216 2038.3
## + parent_marital_status:is_first_child    3     20.53 13309 2038.5
## + ethnic_group:lunch_type                 4     62.42 13267 2038.6
## + parent_marital_status:writing_score     3     11.65 13318 2038.9
## + parent_marital_status:reading_score     3      8.91 13321 2039.0
## - ethnic_group:is_first_child             4    312.27 13642 2039.1
## + ethnic_group:transport_means            4     51.18 13278 2039.1
## - is_first_child:wkly_study_hours         2    223.45 13553 2039.2
## - practice_sport:reading_score            2    225.25 13555 2039.3
## - practice_sport:writing_score            2    234.98 13564 2039.7
## + ethnic_group:writing_score              4     35.77 13294 2039.8
## + ethnic_group:reading_score              4     28.75 13301 2040.1
## - lunch_type:is_first_child               1    209.39 13539 2040.6
## + gender:parent_educ                      5     50.49 13279 2041.2
## + practice_sport:wkly_study_hours         4      3.07 13326 2041.3
## + parent_marital_status:wkly_study_hours  6     86.77 13243 2041.5
## + ethnic_group:practice_sport             8    151.47 13178 2042.7
## + ethnic_group:parent_educ               20    666.95 12663 2043.1
## + ethnic_group:parent_marital_status     11    248.72 13081 2044.3
## - is_first_child:transport_means          1    305.28 13635 2044.8
## + parent_educ:practice_sport             10    183.02 13146 2045.2
## + ethnic_group:wkly_study_hours           8     72.08 13257 2046.2
## + parent_educ:wkly_study_hours           10    151.79 13178 2046.6
## + parent_educ:parent_marital_status      15    311.64 13018 2049.4
## 
## Step:  AIC=2030.91
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:parent_marital_status        2     36.60 13401 2028.5
## - lunch_type:writing_score                1      0.00 13364 2028.9
## - lunch_type:test_prep                    1      0.02 13364 2028.9
## - lunch_type:reading_score                1      0.02 13364 2028.9
## - gender:lunch_type                       1      0.04 13364 2028.9
## - gender:is_first_child                   1      0.15 13364 2028.9
## - transport_means:reading_score           1      0.60 13365 2028.9
## - test_prep:writing_score                 1      1.39 13365 2029.0
## - gender:transport_means                  1      2.51 13366 2029.0
## - test_prep:reading_score                 1      2.58 13366 2029.0
## - lunch_type:transport_means              1      3.50 13368 2029.1
## - is_first_child:reading_score            1      3.54 13368 2029.1
## - test_prep:is_first_child                1      4.34 13368 2029.1
## - test_prep:wkly_study_hours              2     54.29 13418 2029.3
## - transport_means:writing_score           1      9.02 13373 2029.3
## - gender:reading_score                    1      9.82 13374 2029.3
## - gender:test_prep                        1     11.79 13376 2029.4
## - is_first_child:writing_score            1     15.71 13380 2029.6
## - parent_educ:test_prep                   5    200.59 13565 2029.7
## - wkly_study_hours:writing_score          2     63.99 13428 2029.7
## - lunch_type:practice_sport               2     70.02 13434 2030.0
## - lunch_type:wkly_study_hours             2     79.29 13443 2030.4
## - ethnic_group:test_prep                  4    175.35 13539 2030.6
## <none>                                                13364 2030.9
## - writing_score:reading_score             1     45.82 13410 2030.9
## - gender:writing_score                    1     48.31 13412 2031.0
## - test_prep:parent_marital_status         3    143.50 13508 2031.2
## - parent_marital_status:practice_sport    5    255.60 13620 2032.1
## - parent_educ:transport_means             5    259.50 13624 2032.3
## + practice_sport:transport_means          2     44.73 13319 2032.9
## - wkly_study_hours:reading_score          2    146.97 13511 2033.4
## + practice_sport:is_first_child           2     34.43 13330 2033.4
## + gender:wkly_study_hours                 2     21.76 13342 2034.0
## - parent_educ:is_first_child              5    302.38 13666 2034.1
## + transport_means:wkly_study_hours        2     16.34 13348 2034.2
## + gender:practice_sport                   2     16.31 13348 2034.2
## + test_prep:practice_sport                2      4.73 13359 2034.7
## + parent_educ:lunch_type                  5    131.56 13232 2035.1
## + parent_marital_status:transport_means   3     39.56 13324 2035.2
## + gender:parent_marital_status            3     37.39 13327 2035.3
## - test_prep:transport_means               1    147.85 13512 2035.4
## + gender:ethnic_group                     4     76.43 13288 2035.5
## + parent_marital_status:is_first_child    3     25.62 13338 2035.8
## + parent_educ:writing_score               5    115.23 13249 2035.8
## + parent_educ:reading_score               5    109.11 13255 2036.1
## + ethnic_group:lunch_type                 4     58.19 13306 2036.3
## + parent_marital_status:writing_score     3     11.87 13352 2036.4
## + parent_marital_status:reading_score     3      8.66 13355 2036.5
## - is_first_child:wkly_study_hours         2    221.96 13586 2036.6
## - ethnic_group:is_first_child             4    316.00 13680 2036.7
## + ethnic_group:transport_means            4     49.80 13314 2036.7
## + ethnic_group:writing_score              4     34.87 13329 2037.4
## - practice_sport:reading_score            2    243.52 13608 2037.6
## - lunch_type:is_first_child               1    200.99 13565 2037.7
## + ethnic_group:reading_score              4     26.35 13338 2037.8
## - practice_sport:writing_score            2    255.02 13619 2038.1
## + gender:parent_educ                      5     52.34 13312 2038.6
## + practice_sport:wkly_study_hours         4      4.83 13359 2038.7
## + parent_marital_status:wkly_study_hours  6     81.30 13283 2039.3
## + ethnic_group:parent_educ               20    680.64 12683 2040.1
## + ethnic_group:practice_sport             8    144.13 13220 2040.5
## + ethnic_group:parent_marital_status     11    244.59 13119 2042.0
## - is_first_child:transport_means          1    302.40 13666 2042.1
## + parent_educ:practice_sport             10    180.37 13184 2042.9
## + ethnic_group:wkly_study_hours           8     69.56 13294 2043.8
## + parent_educ:wkly_study_hours           10    150.71 13213 2044.2
## + parent_educ:parent_marital_status      15    292.93 13071 2047.8
## 
## Step:  AIC=2028.53
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     lunch_type:writing_score + lunch_type:reading_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:reading_score                1      0.02 13401 2026.5
## - lunch_type:test_prep                    1      0.08 13401 2026.5
## - lunch_type:writing_score                1      0.10 13401 2026.5
## - gender:lunch_type                       1      0.14 13401 2026.5
## - gender:is_first_child                   1      0.27 13401 2026.5
## - transport_means:reading_score           1      0.31 13401 2026.5
## - gender:transport_means                  1      1.75 13402 2026.6
## - test_prep:writing_score                 1      1.77 13402 2026.6
## - is_first_child:reading_score            1      1.82 13402 2026.6
## - test_prep:reading_score                 1      2.65 13403 2026.7
## - lunch_type:transport_means              1      3.16 13404 2026.7
## - test_prep:wkly_study_hours              2     51.47 13452 2026.8
## - test_prep:is_first_child                1      6.34 13407 2026.8
## - gender:test_prep                        1      8.88 13409 2026.9
## - transport_means:writing_score           1     10.11 13411 2027.0
## - gender:reading_score                    1     11.14 13412 2027.0
## - is_first_child:writing_score            1     11.68 13412 2027.0
## - wkly_study_hours:writing_score          2     63.57 13464 2027.3
## - parent_educ:test_prep                   5    202.60 13603 2027.4
## - lunch_type:practice_sport               2     78.52 13479 2028.0
## - ethnic_group:test_prep                  4    171.17 13572 2028.0
## - parent_marital_status:practice_sport    6    265.02 13666 2028.1
## - lunch_type:wkly_study_hours             2     83.97 13484 2028.2
## - writing_score:reading_score             1     44.86 13445 2028.5
## <none>                                                13401 2028.5
## - gender:writing_score                    1     51.15 13452 2028.8
## - test_prep:parent_marital_status         3    145.94 13546 2028.9
## - parent_educ:transport_means             5    257.95 13658 2029.8
## + practice_sport:transport_means          2     45.88 13355 2030.5
## + lunch_type:parent_marital_status        2     36.60 13364 2030.9
## - wkly_study_hours:reading_score          2    147.65 13548 2031.0
## + practice_sport:is_first_child           2     23.73 13377 2031.5
## + gender:wkly_study_hours                 2     17.82 13383 2031.7
## - parent_educ:is_first_child              5    308.05 13709 2031.9
## + transport_means:wkly_study_hours        2     13.15 13387 2032.0
## + gender:practice_sport                   2     13.06 13388 2032.0
## + test_prep:practice_sport                2      4.51 13396 2032.3
## + parent_educ:lunch_type                  5    137.66 13263 2032.4
## + gender:parent_marital_status            3     41.74 13359 2032.7
## - test_prep:transport_means               1    145.91 13546 2032.9
## + parent_marital_status:transport_means   3     36.34 13364 2032.9
## + parent_marital_status:is_first_child    3     28.15 13372 2033.3
## + parent_educ:writing_score               5    115.88 13285 2033.4
## + parent_educ:reading_score               5    112.89 13288 2033.5
## + gender:ethnic_group                     4     67.63 13333 2033.5
## + parent_marital_status:writing_score     3     19.31 13381 2033.7
## - is_first_child:wkly_study_hours         2    209.87 13610 2033.7
## + parent_marital_status:reading_score     3     18.33 13382 2033.7
## + ethnic_group:lunch_type                 4     57.37 13343 2034.0
## - ethnic_group:is_first_child             4    319.51 13720 2034.4
## + ethnic_group:transport_means            4     46.47 13354 2034.5
## - practice_sport:reading_score            2    237.01 13638 2034.9
## + ethnic_group:writing_score              4     35.08 13366 2035.0
## - lunch_type:is_first_child               1    194.82 13595 2035.0
## + ethnic_group:reading_score              4     23.81 13377 2035.5
## - practice_sport:writing_score            2    251.75 13652 2035.5
## + practice_sport:wkly_study_hours         4      5.04 13396 2036.3
## + gender:parent_educ                      5     45.65 13355 2036.5
## + parent_marital_status:wkly_study_hours  6     76.94 13324 2037.1
## + ethnic_group:parent_educ               20    679.69 12721 2037.8
## + ethnic_group:practice_sport             8    149.05 13252 2037.9
## + ethnic_group:parent_marital_status     11    250.46 13150 2039.4
## - is_first_child:transport_means          1    299.95 13700 2039.6
## + parent_educ:practice_sport             10    178.68 13222 2040.6
## + ethnic_group:wkly_study_hours           8     69.52 13331 2041.5
## + parent_educ:wkly_study_hours           10    140.57 13260 2042.3
## + parent_educ:parent_marital_status      15    286.75 13114 2045.8
## 
## Step:  AIC=2026.53
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     lunch_type:writing_score + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:test_prep                    1      0.10 13401 2024.5
## - gender:lunch_type                       1      0.15 13401 2024.5
## - gender:is_first_child                   1      0.27 13401 2024.5
## - transport_means:reading_score           1      0.30 13401 2024.5
## - lunch_type:writing_score                1      0.33 13401 2024.5
## - test_prep:writing_score                 1      1.78 13402 2024.6
## - gender:transport_means                  1      1.79 13402 2024.6
## - is_first_child:reading_score            1      1.87 13402 2024.6
## - test_prep:reading_score                 1      2.66 13403 2024.7
## - lunch_type:transport_means              1      3.17 13404 2024.7
## - test_prep:wkly_study_hours              2     51.51 13452 2024.8
## - test_prep:is_first_child                1      6.33 13407 2024.8
## - gender:test_prep                        1      8.86 13409 2024.9
## - transport_means:writing_score           1     10.30 13411 2025.0
## - gender:reading_score                    1     11.12 13412 2025.0
## - is_first_child:writing_score            1     11.87 13412 2025.0
## - wkly_study_hours:writing_score          2     63.86 13464 2025.3
## - parent_educ:test_prep                   5    202.61 13603 2025.4
## - ethnic_group:test_prep                  4    171.24 13572 2026.0
## - lunch_type:practice_sport               2     79.88 13480 2026.0
## - parent_marital_status:practice_sport    6    265.15 13666 2026.1
## - lunch_type:wkly_study_hours             2     84.14 13485 2026.2
## - writing_score:reading_score             1     44.85 13445 2026.5
## <none>                                                13401 2026.5
## - gender:writing_score                    1     51.14 13452 2026.8
## - test_prep:parent_marital_status         3    145.94 13546 2026.9
## - parent_educ:transport_means             5    257.98 13659 2027.8
## + practice_sport:transport_means          2     45.85 13355 2028.5
## + lunch_type:reading_score                1      0.02 13401 2028.5
## + lunch_type:parent_marital_status        2     36.60 13364 2028.9
## - wkly_study_hours:reading_score          2    148.02 13549 2029.0
## + practice_sport:is_first_child           2     23.74 13377 2029.5
## + gender:wkly_study_hours                 2     17.84 13383 2029.7
## + gender:practice_sport                   2     13.04 13388 2030.0
## + transport_means:wkly_study_hours        2     12.98 13388 2030.0
## - parent_educ:is_first_child              5    309.07 13710 2030.0
## + test_prep:practice_sport                2      4.50 13396 2030.3
## + parent_educ:lunch_type                  5    137.51 13263 2030.4
## + gender:parent_marital_status            3     41.72 13359 2030.7
## - test_prep:transport_means               1    145.99 13547 2030.9
## + parent_marital_status:transport_means   3     36.21 13364 2030.9
## + parent_marital_status:is_first_child    3     28.04 13372 2031.3
## + parent_educ:writing_score               5    115.76 13285 2031.4
## + parent_educ:reading_score               5    112.74 13288 2031.5
## + gender:ethnic_group                     4     67.47 13333 2031.5
## + parent_marital_status:writing_score     3     19.29 13381 2031.7
## - is_first_child:wkly_study_hours         2    209.89 13610 2031.7
## + parent_marital_status:reading_score     3     18.30 13382 2031.7
## + ethnic_group:lunch_type                 4     55.42 13345 2032.1
## - ethnic_group:is_first_child             4    319.50 13720 2032.4
## + ethnic_group:transport_means            4     46.35 13354 2032.5
## - practice_sport:reading_score            2    237.00 13638 2032.9
## + ethnic_group:writing_score              4     35.00 13366 2033.0
## - lunch_type:is_first_child               1    195.72 13596 2033.1
## + ethnic_group:reading_score              4     23.77 13377 2033.5
## - practice_sport:writing_score            2    251.74 13652 2033.5
## + practice_sport:wkly_study_hours         4      5.05 13396 2034.3
## + gender:parent_educ                      5     45.11 13356 2034.5
## + parent_marital_status:wkly_study_hours  6     76.95 13324 2035.1
## + ethnic_group:practice_sport             8    148.88 13252 2035.9
## + ethnic_group:parent_educ               20    677.01 12724 2035.9
## + ethnic_group:parent_marital_status     11    249.41 13151 2037.4
## - is_first_child:transport_means          1    301.81 13702 2037.7
## + parent_educ:practice_sport             10    178.36 13222 2038.6
## + ethnic_group:wkly_study_hours           8     69.48 13331 2039.5
## + parent_educ:wkly_study_hours           10    140.56 13260 2040.3
## + parent_educ:parent_marital_status      15    285.72 13115 2043.8
## 
## Step:  AIC=2024.53
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:lunch_type + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:lunch_type                       1      0.11 13401 2022.5
## - gender:is_first_child                   1      0.28 13401 2022.5
## - transport_means:reading_score           1      0.30 13401 2022.5
## - lunch_type:writing_score                1      0.56 13401 2022.6
## - test_prep:writing_score                 1      1.69 13402 2022.6
## - gender:transport_means                  1      1.78 13402 2022.6
## - is_first_child:reading_score            1      1.87 13403 2022.6
## - test_prep:reading_score                 1      2.63 13403 2022.7
## - lunch_type:transport_means              1      3.07 13404 2022.7
## - test_prep:wkly_study_hours              2     51.73 13452 2022.8
## - test_prep:is_first_child                1      6.37 13407 2022.8
## - gender:test_prep                        1      9.60 13410 2023.0
## - transport_means:writing_score           1     10.27 13411 2023.0
## - gender:reading_score                    1     11.16 13412 2023.0
## - is_first_child:writing_score            1     11.87 13413 2023.1
## - wkly_study_hours:writing_score          2     63.99 13465 2023.3
## - parent_educ:test_prep                   5    202.51 13603 2023.4
## - lunch_type:practice_sport               2     79.98 13481 2024.0
## - parent_marital_status:practice_sport    6    265.09 13666 2024.1
## - ethnic_group:test_prep                  4    173.01 13574 2024.1
## - lunch_type:wkly_study_hours             2     84.04 13485 2024.2
## - writing_score:reading_score             1     45.50 13446 2024.5
## <none>                                                13401 2024.5
## - gender:writing_score                    1     51.51 13452 2024.8
## - test_prep:parent_marital_status         3    146.34 13547 2024.9
## - parent_educ:transport_means             5    259.11 13660 2025.8
## + practice_sport:transport_means          2     45.69 13355 2026.5
## + lunch_type:test_prep                    1      0.10 13401 2026.5
## + lunch_type:reading_score                1      0.04 13401 2026.5
## + lunch_type:parent_marital_status        2     36.68 13364 2026.9
## - wkly_study_hours:reading_score          2    148.13 13549 2027.0
## + practice_sport:is_first_child           2     23.72 13377 2027.5
## + gender:wkly_study_hours                 2     17.79 13383 2027.8
## + gender:practice_sport                   2     13.08 13388 2028.0
## + transport_means:wkly_study_hours        2     13.08 13388 2028.0
## - parent_educ:is_first_child              5    312.25 13713 2028.1
## + test_prep:practice_sport                2      4.57 13396 2028.3
## + parent_educ:lunch_type                  5    137.51 13263 2028.5
## + gender:parent_marital_status            3     41.25 13359 2028.7
## - test_prep:transport_means               1    145.95 13547 2028.9
## + parent_marital_status:transport_means   3     36.01 13365 2029.0
## + parent_marital_status:is_first_child    3     28.06 13373 2029.3
## + parent_educ:writing_score               5    115.77 13285 2029.4
## + parent_educ:reading_score               5    112.72 13288 2029.5
## + gender:ethnic_group                     4     67.34 13333 2029.6
## + parent_marital_status:writing_score     3     19.35 13381 2029.7
## - is_first_child:wkly_study_hours         2    209.83 13610 2029.7
## + parent_marital_status:reading_score     3     18.36 13382 2029.7
## + ethnic_group:lunch_type                 4     55.43 13345 2030.1
## - ethnic_group:is_first_child             4    319.51 13720 2030.4
## + ethnic_group:transport_means            4     45.43 13355 2030.5
## - practice_sport:reading_score            2    237.93 13639 2030.9
## + ethnic_group:writing_score              4     34.93 13366 2031.0
## - lunch_type:is_first_child               1    195.93 13597 2031.1
## + ethnic_group:reading_score              4     23.62 13377 2031.5
## - practice_sport:writing_score            2    252.60 13653 2031.5
## + practice_sport:wkly_study_hours         4      5.14 13396 2032.3
## + gender:parent_educ                      5     45.20 13356 2032.5
## + parent_marital_status:wkly_study_hours  6     76.90 13324 2033.1
## + ethnic_group:practice_sport             8    147.55 13253 2034.0
## + ethnic_group:parent_educ               20    674.97 12726 2034.0
## + ethnic_group:parent_marital_status     11    248.92 13152 2035.5
## - is_first_child:transport_means          1    303.01 13704 2035.7
## + parent_educ:practice_sport             10    176.98 13224 2036.7
## + ethnic_group:wkly_study_hours           8     69.32 13331 2037.5
## + parent_educ:wkly_study_hours           10    140.65 13260 2038.3
## + parent_educ:parent_marital_status      15    282.38 13118 2042.0
## 
## Step:  AIC=2022.54
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:is_first_child + gender:transport_means + 
##     gender:writing_score + gender:reading_score + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + parent_educ:test_prep + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:is_first_child                   1      0.29 13401 2020.5
## - transport_means:reading_score           1      0.33 13401 2020.5
## - lunch_type:writing_score                1      0.81 13402 2020.6
## - test_prep:writing_score                 1      1.67 13402 2020.6
## - gender:transport_means                  1      1.79 13403 2020.6
## - is_first_child:reading_score            1      1.86 13403 2020.6
## - test_prep:reading_score                 1      2.61 13403 2020.7
## - lunch_type:transport_means              1      3.02 13404 2020.7
## - test_prep:is_first_child                1      6.41 13407 2020.8
## - test_prep:wkly_study_hours              2     52.04 13453 2020.8
## - gender:test_prep                        1      9.96 13411 2021.0
## - transport_means:writing_score           1     10.17 13411 2021.0
## - gender:reading_score                    1     11.17 13412 2021.0
## - is_first_child:writing_score            1     11.88 13413 2021.1
## - wkly_study_hours:writing_score          2     64.73 13466 2021.4
## - parent_educ:test_prep                   5    202.45 13603 2021.4
## - lunch_type:practice_sport               2     79.87 13481 2022.0
## - parent_marital_status:practice_sport    6    265.66 13666 2022.1
## - ethnic_group:test_prep                  4    173.39 13574 2022.1
## - lunch_type:wkly_study_hours             2     84.55 13485 2022.2
## <none>                                                13401 2022.5
## - writing_score:reading_score             1     45.63 13446 2022.5
## - gender:writing_score                    1     52.72 13454 2022.9
## - test_prep:parent_marital_status         3    146.27 13547 2022.9
## - parent_educ:transport_means             5    259.00 13660 2023.8
## + practice_sport:transport_means          2     45.63 13355 2024.5
## + gender:lunch_type                       1      0.11 13401 2024.5
## + lunch_type:test_prep                    1      0.06 13401 2024.5
## + lunch_type:reading_score                1      0.05 13401 2024.5
## + lunch_type:parent_marital_status        2     36.73 13364 2024.9
## - wkly_study_hours:reading_score          2    149.86 13551 2025.1
## + practice_sport:is_first_child           2     23.30 13378 2025.5
## + gender:wkly_study_hours                 2     17.89 13383 2025.8
## + gender:practice_sport                   2     13.14 13388 2026.0
## + transport_means:wkly_study_hours        2     13.03 13388 2026.0
## - parent_educ:is_first_child              5    314.56 13715 2026.2
## + test_prep:practice_sport                2      4.54 13396 2026.3
## + parent_educ:lunch_type                  5    137.60 13263 2026.5
## + gender:parent_marital_status            3     41.35 13359 2026.7
## - test_prep:transport_means               1    146.19 13547 2026.9
## + parent_marital_status:transport_means   3     36.03 13365 2027.0
## + parent_marital_status:is_first_child    3     28.08 13373 2027.3
## + parent_educ:writing_score               5    115.63 13285 2027.4
## + parent_educ:reading_score               5    112.57 13288 2027.6
## + gender:ethnic_group                     4     67.12 13334 2027.6
## + parent_marital_status:writing_score     3     19.30 13382 2027.7
## - is_first_child:wkly_study_hours         2    209.75 13610 2027.7
## + parent_marital_status:reading_score     3     18.35 13382 2027.7
## + ethnic_group:lunch_type                 4     55.52 13345 2028.1
## - ethnic_group:is_first_child             4    319.46 13720 2028.4
## + ethnic_group:transport_means            4     45.00 13356 2028.5
## - practice_sport:reading_score            2    237.83 13639 2028.9
## + ethnic_group:writing_score              4     34.30 13366 2029.0
## - lunch_type:is_first_child               1    195.90 13597 2029.1
## + ethnic_group:reading_score              4     23.46 13377 2029.5
## - practice_sport:writing_score            2    252.59 13653 2029.6
## + practice_sport:wkly_study_hours         4      5.10 13396 2030.3
## + gender:parent_educ                      5     45.20 13356 2030.5
## + parent_marital_status:wkly_study_hours  6     76.10 13325 2031.2
## + ethnic_group:practice_sport             8    147.59 13253 2032.0
## + ethnic_group:parent_educ               20    675.07 12726 2032.0
## + ethnic_group:parent_marital_status     11    249.02 13152 2033.5
## - is_first_child:transport_means          1    303.18 13704 2033.7
## + parent_educ:practice_sport             10    176.55 13224 2034.7
## + ethnic_group:wkly_study_hours           8     69.43 13331 2035.5
## + parent_educ:wkly_study_hours           10    138.61 13262 2036.4
## + parent_educ:parent_marital_status      15    280.46 13120 2040.1
## 
## Step:  AIC=2020.55
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + transport_means:reading_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - transport_means:reading_score           1      0.30 13401 2018.6
## - lunch_type:writing_score                1      0.85 13402 2018.6
## - test_prep:writing_score                 1      1.63 13403 2018.6
## - gender:transport_means                  1      1.78 13403 2018.6
## - is_first_child:reading_score            1      2.10 13403 2018.6
## - test_prep:reading_score                 1      2.63 13404 2018.7
## - lunch_type:transport_means              1      3.11 13404 2018.7
## - test_prep:is_first_child                1      6.13 13407 2018.8
## - test_prep:wkly_study_hours              2     52.09 13453 2018.8
## - gender:test_prep                        1     10.01 13411 2019.0
## - transport_means:writing_score           1     10.34 13411 2019.0
## - gender:reading_score                    1     11.07 13412 2019.0
## - is_first_child:writing_score            1     13.46 13414 2019.1
## - wkly_study_hours:writing_score          2     64.45 13466 2019.4
## - parent_educ:test_prep                   5    202.40 13604 2019.4
## - lunch_type:practice_sport               2     80.03 13481 2020.1
## - parent_marital_status:practice_sport    6    265.39 13666 2020.1
## - ethnic_group:test_prep                  4    173.41 13574 2020.1
## - lunch_type:wkly_study_hours             2     84.50 13486 2020.3
## - writing_score:reading_score             1     45.36 13446 2020.5
## <none>                                                13401 2020.5
## - gender:writing_score                    1     52.66 13454 2020.9
## - test_prep:parent_marital_status         3    146.27 13547 2021.0
## - parent_educ:transport_means             5    259.51 13661 2021.9
## + gender:is_first_child                   1      0.29 13401 2022.5
## + gender:lunch_type                       1      0.12 13401 2022.5
## + lunch_type:test_prep                    1      0.07 13401 2022.5
## + lunch_type:reading_score                1      0.05 13401 2022.5
## + practice_sport:transport_means          2     45.23 13356 2022.6
## + lunch_type:parent_marital_status        2     36.87 13364 2022.9
## - wkly_study_hours:reading_score          2    149.91 13551 2023.1
## + practice_sport:is_first_child           2     23.06 13378 2023.5
## + gender:wkly_study_hours                 2     17.86 13383 2023.8
## + gender:practice_sport                   2     13.37 13388 2024.0
## + transport_means:wkly_study_hours        2     13.28 13388 2024.0
## - parent_educ:is_first_child              5    314.98 13716 2024.3
## + test_prep:practice_sport                2      4.37 13397 2024.4
## + parent_educ:lunch_type                  5    136.71 13264 2024.5
## + gender:parent_marital_status            3     41.50 13360 2024.7
## - test_prep:transport_means               1    146.02 13547 2025.0
## + parent_marital_status:transport_means   3     35.91 13365 2025.0
## + parent_marital_status:is_first_child    3     28.30 13373 2025.3
## + parent_educ:writing_score               5    115.86 13285 2025.4
## + parent_educ:reading_score               5    112.81 13288 2025.6
## + gender:ethnic_group                     4     66.90 13334 2025.6
## + parent_marital_status:writing_score     3     19.31 13382 2025.7
## - is_first_child:wkly_study_hours         2    209.47 13610 2025.7
## + parent_marital_status:reading_score     3     18.31 13383 2025.7
## + ethnic_group:lunch_type                 4     54.85 13346 2026.1
## - ethnic_group:is_first_child             4    319.53 13721 2026.5
## + ethnic_group:transport_means            4     45.15 13356 2026.6
## - practice_sport:reading_score            2    237.58 13639 2026.9
## + ethnic_group:writing_score              4     34.51 13367 2027.0
## - lunch_type:is_first_child               1    201.39 13602 2027.3
## + ethnic_group:reading_score              4     23.63 13378 2027.5
## - practice_sport:writing_score            2    252.32 13653 2027.6
## + practice_sport:wkly_study_hours         4      5.14 13396 2028.3
## + gender:parent_educ                      5     45.13 13356 2028.6
## + parent_marital_status:wkly_study_hours  6     74.72 13326 2029.2
## + ethnic_group:practice_sport             8    147.69 13253 2030.0
## + ethnic_group:parent_educ               20    670.46 12731 2030.3
## + ethnic_group:parent_marital_status     11    249.28 13152 2031.5
## - is_first_child:transport_means          1    305.24 13706 2031.8
## + parent_educ:practice_sport             10    176.82 13224 2032.7
## + ethnic_group:wkly_study_hours           8     69.67 13331 2033.5
## + parent_educ:wkly_study_hours           10    138.77 13262 2034.4
## + parent_educ:parent_marital_status      15    280.68 13120 2038.1
## 
## Step:  AIC=2018.56
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:writing_score                1      0.78 13402 2016.6
## - test_prep:writing_score                 1      1.90 13403 2016.7
## - is_first_child:reading_score            1      2.11 13404 2016.7
## - gender:transport_means                  1      2.15 13404 2016.7
## - test_prep:reading_score                 1      3.00 13404 2016.7
## - lunch_type:transport_means              1      3.31 13405 2016.7
## - test_prep:is_first_child                1      6.25 13408 2016.8
## - test_prep:wkly_study_hours              2     51.80 13453 2016.8
## - gender:test_prep                        1     10.14 13412 2017.0
## - gender:reading_score                    1     11.43 13413 2017.1
## - is_first_child:writing_score            1     13.54 13415 2017.2
## - wkly_study_hours:writing_score          2     64.15 13466 2017.4
## - parent_educ:test_prep                   5    202.42 13604 2017.4
## - lunch_type:practice_sport               2     80.54 13482 2018.1
## - ethnic_group:test_prep                  4    173.28 13575 2018.1
## - parent_marital_status:practice_sport    6    268.00 13669 2018.2
## - lunch_type:wkly_study_hours             2     85.22 13487 2018.3
## <none>                                                13401 2018.6
## - writing_score:reading_score             1     45.74 13447 2018.6
## - gender:writing_score                    1     53.68 13455 2018.9
## - test_prep:parent_marital_status         3    146.02 13547 2019.0
## - parent_educ:transport_means             5    267.05 13668 2020.2
## + transport_means:reading_score           1      0.30 13401 2020.5
## + gender:is_first_child                   1      0.25 13401 2020.5
## + gender:lunch_type                       1      0.15 13401 2020.6
## + lunch_type:test_prep                    1      0.07 13401 2020.6
## + lunch_type:reading_score                1      0.04 13401 2020.6
## + practice_sport:transport_means          2     45.27 13356 2020.6
## + lunch_type:parent_marital_status        2     36.56 13365 2021.0
## - wkly_study_hours:reading_score          2    149.72 13551 2021.1
## + practice_sport:is_first_child           2     23.23 13378 2021.5
## + gender:wkly_study_hours                 2     17.67 13384 2021.8
## + transport_means:wkly_study_hours        2     13.23 13388 2022.0
## + gender:practice_sport                   2     13.05 13388 2022.0
## - parent_educ:is_first_child              5    315.01 13716 2022.3
## + test_prep:practice_sport                2      4.44 13397 2022.4
## + parent_educ:lunch_type                  5    135.06 13266 2022.6
## + gender:parent_marital_status            3     41.19 13360 2022.8
## + parent_marital_status:transport_means   3     35.46 13366 2023.0
## - transport_means:writing_score           1    153.47 13555 2023.3
## + parent_marital_status:is_first_child    3     28.33 13373 2023.3
## + parent_educ:writing_score               5    116.06 13285 2023.4
## - test_prep:transport_means               1    160.61 13562 2023.6
## + gender:ethnic_group                     4     67.17 13334 2023.6
## + parent_educ:reading_score               5    112.21 13289 2023.6
## - is_first_child:wkly_study_hours         2    209.18 13611 2023.7
## + parent_marital_status:writing_score     3     19.23 13382 2023.7
## + parent_marital_status:reading_score     3     18.17 13383 2023.8
## + ethnic_group:lunch_type                 4     55.15 13346 2024.1
## - ethnic_group:is_first_child             4    319.71 13721 2024.5
## + ethnic_group:transport_means            4     45.31 13356 2024.6
## + ethnic_group:writing_score              4     34.49 13367 2025.0
## - practice_sport:reading_score            2    241.64 13643 2025.1
## - lunch_type:is_first_child               1    201.69 13603 2025.4
## + ethnic_group:reading_score              4     23.61 13378 2025.5
## - practice_sport:writing_score            2    255.57 13657 2025.7
## + practice_sport:wkly_study_hours         4      5.04 13396 2026.3
## + gender:parent_educ                      5     45.33 13356 2026.6
## + parent_marital_status:wkly_study_hours  6     73.70 13328 2027.3
## + ethnic_group:practice_sport             8    147.99 13253 2028.0
## + ethnic_group:parent_educ               20    670.76 12731 2028.3
## + ethnic_group:parent_marital_status     11    249.58 13152 2029.5
## - is_first_child:transport_means          1    305.44 13707 2029.9
## + parent_educ:practice_sport             10    174.59 13227 2030.8
## + ethnic_group:wkly_study_hours           8     69.42 13332 2031.5
## + parent_educ:wkly_study_hours           10    138.74 13263 2032.4
## + parent_educ:parent_marital_status      15    280.74 13121 2036.1
## 
## Step:  AIC=2016.6
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:writing_score                 1      1.80 13404 2014.7
## - is_first_child:reading_score            1      2.10 13404 2014.7
## - gender:transport_means                  1      2.15 13404 2014.7
## - test_prep:reading_score                 1      2.78 13405 2014.7
## - lunch_type:transport_means              1      3.36 13406 2014.8
## - test_prep:is_first_child                1      6.16 13408 2014.9
## - test_prep:wkly_study_hours              2     52.32 13454 2014.9
## - gender:test_prep                        1     10.26 13412 2015.0
## - gender:reading_score                    1     11.86 13414 2015.1
## - is_first_child:writing_score            1     13.43 13416 2015.2
## - parent_educ:test_prep                   5    201.91 13604 2015.4
## - wkly_study_hours:writing_score          2     65.71 13468 2015.5
## - lunch_type:practice_sport               2     80.69 13483 2016.1
## - ethnic_group:test_prep                  4    174.00 13576 2016.2
## - lunch_type:wkly_study_hours             2     84.81 13487 2016.3
## - parent_marital_status:practice_sport    6    273.49 13676 2016.5
## <none>                                                13402 2016.6
## - gender:writing_score                    1     54.11 13456 2017.0
## - test_prep:parent_marital_status         3    146.88 13549 2017.0
## - writing_score:reading_score             1     62.07 13464 2017.3
## - parent_educ:transport_means             5    267.75 13670 2018.3
## + lunch_type:writing_score                1      0.78 13401 2018.6
## + lunch_type:reading_score                1      0.60 13402 2018.6
## + gender:lunch_type                       1      0.42 13402 2018.6
## + gender:is_first_child                   1      0.29 13402 2018.6
## + lunch_type:test_prep                    1      0.28 13402 2018.6
## + transport_means:reading_score           1      0.22 13402 2018.6
## + practice_sport:transport_means          2     45.37 13357 2018.6
## + lunch_type:parent_marital_status        2     36.89 13365 2019.0
## - wkly_study_hours:reading_score          2    152.04 13554 2019.2
## + practice_sport:is_first_child           2     23.35 13379 2019.6
## + gender:wkly_study_hours                 2     17.26 13385 2019.8
## + transport_means:wkly_study_hours        2     13.34 13389 2020.0
## + gender:practice_sport                   2     13.11 13389 2020.0
## - parent_educ:is_first_child              5    315.14 13717 2020.3
## + test_prep:practice_sport                2      4.55 13398 2020.4
## + parent_educ:lunch_type                  5    135.48 13267 2020.6
## + gender:parent_marital_status            3     41.62 13360 2020.8
## + parent_marital_status:transport_means   3     36.01 13366 2021.0
## + parent_marital_status:is_first_child    3     28.98 13373 2021.3
## - transport_means:writing_score           1    154.60 13557 2021.4
## + parent_educ:writing_score               5    115.08 13287 2021.5
## + gender:ethnic_group                     4     66.83 13335 2021.7
## - is_first_child:wkly_study_hours         2    208.64 13611 2021.7
## + parent_educ:reading_score               5    110.17 13292 2021.7
## - test_prep:transport_means               1    163.34 13566 2021.8
## + parent_marital_status:writing_score     3     18.73 13383 2021.8
## + parent_marital_status:reading_score     3     17.60 13385 2021.8
## + ethnic_group:lunch_type                 4     55.53 13347 2022.2
## + ethnic_group:transport_means            4     45.91 13356 2022.6
## - ethnic_group:is_first_child             4    322.31 13724 2022.6
## + ethnic_group:writing_score              4     33.95 13368 2023.1
## - practice_sport:reading_score            2    243.53 13646 2023.2
## + ethnic_group:reading_score              4     22.78 13379 2023.6
## - lunch_type:is_first_child               1    207.00 13609 2023.6
## - practice_sport:writing_score            2    257.04 13659 2023.8
## + practice_sport:wkly_study_hours         4      5.31 13397 2024.4
## + gender:parent_educ                      5     44.90 13357 2024.6
## + parent_marital_status:wkly_study_hours  6     73.14 13329 2025.4
## + ethnic_group:practice_sport             8    148.36 13254 2026.0
## + ethnic_group:parent_educ               20    671.07 12731 2026.3
## + ethnic_group:parent_marital_status     11    250.28 13152 2027.5
## - is_first_child:transport_means          1    309.57 13712 2028.1
## + parent_educ:practice_sport             10    174.89 13227 2028.8
## + ethnic_group:wkly_study_hours           8     70.01 13332 2029.5
## + parent_educ:wkly_study_hours           10    138.31 13264 2030.5
## + parent_educ:parent_marital_status      15    281.10 13121 2034.1
## 
## Step:  AIC=2014.68
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     test_prep:reading_score + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:reading_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:reading_score                 1      1.48 13405 2012.7
## - is_first_child:reading_score            1      1.63 13406 2012.8
## - gender:transport_means                  1      2.34 13406 2012.8
## - lunch_type:transport_means              1      3.39 13407 2012.8
## - test_prep:is_first_child                1      6.16 13410 2013.0
## - test_prep:wkly_study_hours              2     52.00 13456 2013.0
## - gender:reading_score                    1     11.46 13415 2013.2
## - is_first_child:writing_score            1     12.46 13416 2013.2
## - gender:test_prep                        1     12.89 13417 2013.2
## - parent_educ:test_prep                   5    200.38 13604 2013.4
## - wkly_study_hours:writing_score          2     67.14 13471 2013.6
## - lunch_type:practice_sport               2     79.31 13483 2014.2
## - lunch_type:wkly_study_hours             2     84.80 13489 2014.4
## - parent_marital_status:practice_sport    6    274.52 13678 2014.6
## <none>                                                13404 2014.7
## - gender:writing_score                    1     53.43 13457 2015.0
## - ethnic_group:test_prep                  4    193.39 13597 2015.1
## - test_prep:parent_marital_status         3    150.75 13555 2015.3
## - writing_score:reading_score             1     60.73 13465 2015.3
## - parent_educ:transport_means             5    268.91 13673 2016.4
## + test_prep:writing_score                 1      1.80 13402 2016.6
## + practice_sport:transport_means          2     46.67 13357 2016.6
## + lunch_type:writing_score                1      0.68 13403 2016.7
## + lunch_type:reading_score                1      0.54 13403 2016.7
## + transport_means:reading_score           1      0.46 13404 2016.7
## + gender:lunch_type                       1      0.37 13404 2016.7
## + gender:is_first_child                   1      0.24 13404 2016.7
## + lunch_type:test_prep                    1      0.10 13404 2016.7
## + lunch_type:parent_marital_status        2     36.97 13367 2017.0
## - wkly_study_hours:reading_score          2    155.27 13559 2017.5
## + practice_sport:is_first_child           2     23.61 13380 2017.6
## + gender:wkly_study_hours                 2     16.79 13387 2017.9
## + transport_means:wkly_study_hours        2     13.53 13390 2018.1
## + gender:practice_sport                   2     13.12 13391 2018.1
## - parent_educ:is_first_child              5    313.40 13717 2018.3
## + test_prep:practice_sport                2      5.53 13398 2018.4
## + parent_educ:lunch_type                  5    135.26 13269 2018.7
## + gender:parent_marital_status            3     42.36 13362 2018.8
## + parent_marital_status:transport_means   3     35.66 13368 2019.1
## - transport_means:writing_score           1    152.97 13557 2019.4
## + parent_marital_status:is_first_child    3     28.97 13375 2019.4
## + gender:ethnic_group                     4     67.38 13337 2019.7
## + parent_educ:writing_score               5    110.59 13293 2019.8
## - is_first_child:wkly_study_hours         2    209.20 13613 2019.8
## - test_prep:transport_means               1    163.34 13567 2019.8
## + parent_marital_status:writing_score     3     18.60 13385 2019.9
## + parent_marital_status:reading_score     3     17.26 13387 2019.9
## + parent_educ:reading_score               5    106.92 13297 2020.0
## + ethnic_group:lunch_type                 4     55.27 13349 2020.2
## - ethnic_group:is_first_child             4    321.63 13726 2020.7
## + ethnic_group:transport_means            4     43.59 13360 2020.8
## + ethnic_group:writing_score              4     34.31 13370 2021.2
## - practice_sport:reading_score            2    243.55 13648 2021.3
## + ethnic_group:reading_score              4     22.60 13381 2021.7
## - lunch_type:is_first_child               1    206.88 13611 2021.7
## - practice_sport:writing_score            2    256.75 13661 2021.9
## + practice_sport:wkly_study_hours         4      5.46 13398 2022.4
## + gender:parent_educ                      5     44.77 13359 2022.7
## + parent_marital_status:wkly_study_hours  6     72.82 13331 2023.5
## + ethnic_group:practice_sport             8    147.13 13257 2024.2
## + ethnic_group:parent_educ               20    668.09 12736 2024.5
## + ethnic_group:parent_marital_status     11    252.05 13152 2025.5
## - is_first_child:transport_means          1    313.06 13717 2026.3
## + parent_educ:practice_sport             10    170.36 13234 2027.1
## + ethnic_group:wkly_study_hours           8     70.97 13333 2027.5
## + parent_educ:wkly_study_hours           10    137.80 13266 2028.6
## + parent_educ:parent_marital_status      15    281.80 13122 2032.1
## 
## Step:  AIC=2012.74
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:reading_score + transport_means:writing_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - is_first_child:reading_score            1      1.32 13407 2010.8
## - gender:transport_means                  1      2.24 13408 2010.8
## - lunch_type:transport_means              1      3.50 13409 2010.9
## - test_prep:is_first_child                1      6.72 13412 2011.0
## - test_prep:wkly_study_hours              2     53.19 13459 2011.1
## - gender:test_prep                        1     11.43 13417 2011.2
## - is_first_child:writing_score            1     11.68 13417 2011.3
## - gender:reading_score                    1     11.96 13417 2011.3
## - parent_educ:test_prep                   5    199.26 13605 2011.5
## - wkly_study_hours:writing_score          2     68.28 13474 2011.7
## - lunch_type:practice_sport               2     79.01 13484 2012.2
## - lunch_type:wkly_study_hours             2     84.35 13490 2012.4
## - parent_marital_status:practice_sport    6    274.75 13680 2012.7
## <none>                                                13405 2012.7
## - gender:writing_score                    1     53.22 13459 2013.1
## - ethnic_group:test_prep                  4    193.34 13599 2013.2
## - test_prep:parent_marital_status         3    149.39 13555 2013.3
## - writing_score:reading_score             1     78.86 13484 2014.2
## - parent_educ:transport_means             5    270.25 13676 2014.5
## + practice_sport:transport_means          2     47.08 13358 2014.7
## + test_prep:reading_score                 1      1.48 13404 2014.7
## + transport_means:reading_score           1      0.55 13405 2014.7
## + test_prep:writing_score                 1      0.50 13405 2014.7
## + lunch_type:writing_score                1      0.45 13405 2014.7
## + lunch_type:test_prep                    1      0.41 13405 2014.7
## + gender:is_first_child                   1      0.39 13405 2014.7
## + gender:lunch_type                       1      0.31 13405 2014.7
## + lunch_type:reading_score                1      0.30 13405 2014.7
## + lunch_type:parent_marital_status        2     36.37 13369 2015.1
## - wkly_study_hours:reading_score          2    157.93 13563 2015.7
## + practice_sport:is_first_child           2     23.45 13382 2015.7
## + gender:wkly_study_hours                 2     17.05 13388 2016.0
## + transport_means:wkly_study_hours        2     14.14 13391 2016.1
## + gender:practice_sport                   2     13.30 13392 2016.2
## + test_prep:practice_sport                2      5.51 13400 2016.5
## - parent_educ:is_first_child              5    318.31 13724 2016.6
## + parent_educ:lunch_type                  5    134.20 13271 2016.8
## + gender:parent_marital_status            3     43.04 13362 2016.8
## + parent_marital_status:transport_means   3     36.04 13369 2017.2
## + parent_marital_status:is_first_child    3     29.52 13376 2017.4
## - transport_means:writing_score           1    157.82 13563 2017.7
## + gender:ethnic_group                     4     66.04 13339 2017.8
## + parent_educ:writing_score               5    110.79 13295 2017.8
## - is_first_child:wkly_study_hours         2    209.58 13615 2017.9
## - test_prep:transport_means               1    164.22 13570 2017.9
## + parent_marital_status:writing_score     3     18.30 13387 2017.9
## + parent_marital_status:reading_score     3     16.89 13389 2018.0
## + parent_educ:reading_score               5    107.28 13298 2018.0
## + ethnic_group:lunch_type                 4     55.80 13350 2018.3
## + ethnic_group:transport_means            4     43.00 13362 2018.8
## - ethnic_group:is_first_child             4    324.69 13730 2018.9
## + ethnic_group:writing_score              4     33.39 13372 2019.3
## - practice_sport:reading_score            2    243.58 13649 2019.4
## - lunch_type:is_first_child               1    206.22 13612 2019.8
## + ethnic_group:reading_score              4     20.87 13385 2019.8
## - practice_sport:writing_score            2    258.40 13664 2020.0
## + practice_sport:wkly_study_hours         4      5.46 13400 2020.5
## + gender:parent_educ                      5     43.20 13362 2020.8
## + parent_marital_status:wkly_study_hours  6     72.52 13333 2021.5
## + ethnic_group:practice_sport             8    148.07 13257 2022.2
## + ethnic_group:parent_educ               20    669.54 12736 2022.5
## + ethnic_group:parent_marital_status     11    252.99 13152 2023.5
## - is_first_child:transport_means          1    315.45 13721 2024.5
## + parent_educ:practice_sport             10    170.06 13235 2025.2
## + ethnic_group:wkly_study_hours           8     72.01 13333 2025.6
## + parent_educ:wkly_study_hours           10    138.74 13267 2026.6
## + parent_educ:parent_marital_status      15    282.44 13123 2030.2
## 
## Step:  AIC=2010.8
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:transport_means + gender:writing_score + 
##     gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:transport_means                  1      2.06 13409 2008.9
## - lunch_type:transport_means              1      3.14 13410 2008.9
## - test_prep:wkly_study_hours              2     52.37 13459 2009.1
## - test_prep:is_first_child                1      8.30 13415 2009.2
## - gender:test_prep                        1     10.98 13418 2009.3
## - gender:reading_score                    1     11.21 13418 2009.3
## - parent_educ:test_prep                   5    199.40 13606 2009.5
## - wkly_study_hours:writing_score          2     67.61 13474 2009.8
## - lunch_type:practice_sport               2     79.15 13486 2010.3
## - lunch_type:wkly_study_hours             2     84.09 13491 2010.5
## - parent_marital_status:practice_sport    6    274.31 13681 2010.8
## <none>                                                13407 2010.8
## - gender:writing_score                    1     51.99 13459 2011.1
## - ethnic_group:test_prep                  4    192.05 13599 2011.2
## - test_prep:parent_marital_status         3    148.25 13555 2011.3
## - is_first_child:writing_score            1     64.27 13471 2011.6
## - writing_score:reading_score             1     78.91 13486 2012.3
## - parent_educ:transport_means             5    269.60 13676 2012.5
## + practice_sport:transport_means          2     47.48 13359 2012.7
## + is_first_child:reading_score            1      1.32 13405 2012.7
## + test_prep:reading_score                 1      1.17 13406 2012.8
## + gender:is_first_child                   1      0.59 13406 2012.8
## + transport_means:reading_score           1      0.52 13406 2012.8
## + lunch_type:writing_score                1      0.47 13406 2012.8
## + test_prep:writing_score                 1      0.41 13406 2012.8
## + lunch_type:test_prep                    1      0.40 13406 2012.8
## + gender:lunch_type                       1      0.32 13406 2012.8
## + lunch_type:reading_score                1      0.28 13406 2012.8
## + lunch_type:parent_marital_status        2     35.04 13372 2013.3
## - wkly_study_hours:reading_score          2    157.14 13564 2013.7
## + practice_sport:is_first_child           2     24.67 13382 2013.7
## + gender:wkly_study_hours                 2     16.60 13390 2014.1
## + transport_means:wkly_study_hours        2     13.64 13393 2014.2
## + gender:practice_sport                   2     13.42 13393 2014.2
## + test_prep:practice_sport                2      5.30 13402 2014.6
## - parent_educ:is_first_child              5    318.85 13726 2014.7
## + parent_educ:lunch_type                  5    135.30 13272 2014.8
## + gender:parent_marital_status            3     42.77 13364 2014.9
## + parent_marital_status:transport_means   3     36.64 13370 2015.2
## + parent_marital_status:is_first_child    3     29.83 13377 2015.5
## - transport_means:writing_score           1    156.59 13563 2015.7
## + parent_educ:writing_score               5    111.81 13295 2015.9
## + gender:ethnic_group                     4     66.37 13340 2015.9
## - is_first_child:wkly_study_hours         2    208.33 13615 2015.9
## - test_prep:transport_means               1    163.89 13571 2016.0
## + parent_marital_status:writing_score     3     18.15 13389 2016.0
## + parent_educ:reading_score               5    108.20 13299 2016.0
## + parent_marital_status:reading_score     3     17.03 13390 2016.0
## + ethnic_group:lunch_type                 4     55.88 13351 2016.3
## - ethnic_group:is_first_child             4    324.74 13732 2016.9
## + ethnic_group:transport_means            4     41.13 13366 2017.0
## - practice_sport:reading_score            2    242.36 13649 2017.4
## + ethnic_group:writing_score              4     32.30 13374 2017.4
## + ethnic_group:reading_score              4     20.14 13387 2017.9
## - lunch_type:is_first_child               1    208.80 13616 2017.9
## - practice_sport:writing_score            2    257.62 13664 2018.0
## + practice_sport:wkly_study_hours         4      5.13 13402 2018.6
## + gender:parent_educ                      5     42.95 13364 2018.9
## + parent_marital_status:wkly_study_hours  6     72.01 13335 2019.6
## + ethnic_group:practice_sport             8    147.83 13259 2020.3
## + ethnic_group:parent_educ               20    669.07 12738 2020.6
## + ethnic_group:parent_marital_status     11    252.79 13154 2021.6
## - is_first_child:transport_means          1    314.70 13722 2022.5
## + parent_educ:practice_sport             10    168.84 13238 2023.3
## + ethnic_group:wkly_study_hours           8     73.14 13334 2023.6
## + parent_educ:wkly_study_hours           10    138.71 13268 2024.7
## + parent_educ:parent_marital_status      15    281.31 13126 2028.3
## 
## Step:  AIC=2008.89
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:transport_means              1      2.47 13411 2007.0
## - test_prep:wkly_study_hours              2     51.52 13460 2007.2
## - test_prep:is_first_child                1      8.32 13417 2007.3
## - gender:reading_score                    1     11.05 13420 2007.4
## - gender:test_prep                        1     11.75 13421 2007.4
## - parent_educ:test_prep                   5    200.48 13609 2007.7
## - wkly_study_hours:writing_score          2     66.63 13476 2007.8
## - lunch_type:practice_sport               2     78.42 13487 2008.3
## - lunch_type:wkly_study_hours             2     84.36 13493 2008.6
## - parent_marital_status:practice_sport    6    272.93 13682 2008.8
## <none>                                                13409 2008.9
## - gender:writing_score                    1     51.66 13460 2009.2
## - ethnic_group:test_prep                  4    190.47 13599 2009.2
## - test_prep:parent_marital_status         3    147.01 13556 2009.3
## - is_first_child:writing_score            1     64.36 13473 2009.7
## - writing_score:reading_score             1     78.51 13487 2010.3
## - parent_educ:transport_means             5    270.62 13679 2010.7
## + practice_sport:transport_means          2     47.94 13361 2010.8
## + gender:transport_means                  1      2.06 13407 2010.8
## + is_first_child:reading_score            1      1.14 13408 2010.8
## + test_prep:reading_score                 1      1.10 13408 2010.8
## + transport_means:reading_score           1      0.97 13408 2010.8
## + gender:is_first_child                   1      0.53 13408 2010.9
## + lunch_type:writing_score                1      0.48 13408 2010.9
## + gender:lunch_type                       1      0.36 13408 2010.9
## + lunch_type:test_prep                    1      0.34 13408 2010.9
## + test_prep:writing_score                 1      0.34 13408 2010.9
## + lunch_type:reading_score                1      0.25 13409 2010.9
## + lunch_type:parent_marital_status        2     34.26 13375 2011.4
## - wkly_study_hours:reading_score          2    155.67 13564 2011.7
## + practice_sport:is_first_child           2     24.47 13384 2011.8
## + gender:wkly_study_hours                 2     16.66 13392 2012.2
## + transport_means:wkly_study_hours        2     13.48 13395 2012.3
## + gender:practice_sport                   2     13.45 13395 2012.3
## + test_prep:practice_sport                2      5.19 13404 2012.7
## - parent_educ:is_first_child              5    316.99 13726 2012.7
## + parent_educ:lunch_type                  5    137.01 13272 2012.8
## + gender:parent_marital_status            3     42.45 13366 2013.0
## + parent_marital_status:transport_means   3     36.04 13373 2013.3
## + parent_marital_status:is_first_child    3     28.82 13380 2013.6
## + parent_educ:writing_score               5    112.23 13297 2013.9
## + gender:ethnic_group                     4     66.45 13342 2014.0
## - transport_means:writing_score           1    161.84 13571 2014.0
## - test_prep:transport_means               1    162.13 13571 2014.0
## + parent_educ:reading_score               5    109.25 13300 2014.1
## + parent_marital_status:writing_score     3     17.59 13391 2014.1
## - is_first_child:wkly_study_hours         2    211.72 13620 2014.1
## + parent_marital_status:reading_score     3     16.54 13392 2014.2
## + ethnic_group:lunch_type                 4     55.13 13354 2014.5
## - ethnic_group:is_first_child             4    322.81 13732 2014.9
## + ethnic_group:transport_means            4     42.43 13366 2015.0
## + ethnic_group:writing_score              4     31.82 13377 2015.5
## - practice_sport:reading_score            2    248.84 13658 2015.7
## + ethnic_group:reading_score              4     20.34 13388 2016.0
## - lunch_type:is_first_child               1    212.26 13621 2016.2
## - practice_sport:writing_score            2    265.02 13674 2016.4
## + practice_sport:wkly_study_hours         4      4.86 13404 2016.7
## + gender:parent_educ                      5     43.48 13365 2017.0
## + parent_marital_status:wkly_study_hours  6     71.11 13338 2017.8
## + ethnic_group:practice_sport             8    147.83 13261 2018.3
## + ethnic_group:parent_educ               20    668.14 12741 2018.7
## + ethnic_group:parent_marital_status     11    250.04 13159 2019.8
## - is_first_child:transport_means          1    316.68 13726 2020.7
## + parent_educ:practice_sport             10    170.52 13238 2021.3
## + ethnic_group:wkly_study_hours           8     73.57 13335 2021.7
## + parent_educ:wkly_study_hours           10    139.70 13269 2022.7
## + parent_educ:parent_marital_status      15    274.17 13135 2026.7
## 
## Step:  AIC=2007
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:is_first_child                1      7.83 13419 2005.3
## - test_prep:wkly_study_hours              2     55.11 13466 2005.4
## - gender:reading_score                    1     10.96 13422 2005.5
## - gender:test_prep                        1     11.37 13423 2005.5
## - parent_educ:test_prep                   5    203.23 13614 2005.9
## - wkly_study_hours:writing_score          2     68.75 13480 2006.0
## - lunch_type:practice_sport               2     77.17 13488 2006.4
## - lunch_type:wkly_study_hours             2     83.60 13495 2006.7
## - parent_marital_status:practice_sport    6    272.73 13684 2006.9
## <none>                                                13411 2007.0
## - gender:writing_score                    1     51.26 13462 2007.2
## - ethnic_group:test_prep                  4    191.80 13603 2007.4
## - test_prep:parent_marital_status         3    146.93 13558 2007.4
## - is_first_child:writing_score            1     63.80 13475 2007.8
## - writing_score:reading_score             1     78.83 13490 2008.5
## - parent_educ:transport_means             5    268.35 13680 2008.7
## + lunch_type:transport_means              1      2.47 13409 2008.9
## + practice_sport:transport_means          2     47.08 13364 2008.9
## + gender:transport_means                  1      1.38 13410 2008.9
## + test_prep:reading_score                 1      1.23 13410 2009.0
## + transport_means:reading_score           1      1.16 13410 2009.0
## + is_first_child:reading_score            1      0.86 13410 2009.0
## + gender:is_first_child                   1      0.61 13411 2009.0
## + lunch_type:writing_score                1      0.50 13411 2009.0
## + test_prep:writing_score                 1      0.40 13411 2009.0
## + lunch_type:reading_score                1      0.29 13411 2009.0
## + gender:lunch_type                       1      0.28 13411 2009.0
## + lunch_type:test_prep                    1      0.20 13411 2009.0
## + lunch_type:parent_marital_status        2     33.97 13377 2009.5
## - wkly_study_hours:reading_score          2    158.85 13570 2010.0
## + practice_sport:is_first_child           2     23.86 13387 2010.0
## + gender:wkly_study_hours                 2     16.40 13395 2010.3
## + gender:practice_sport                   2     13.58 13398 2010.4
## + transport_means:wkly_study_hours        2     13.07 13398 2010.4
## - parent_educ:is_first_child              5    315.07 13726 2010.7
## + test_prep:practice_sport                2      5.09 13406 2010.8
## + parent_educ:lunch_type                  5    138.25 13273 2010.9
## + gender:parent_marital_status            3     42.67 13369 2011.1
## + parent_marital_status:transport_means   3     37.05 13374 2011.4
## + parent_marital_status:is_first_child    3     30.11 13381 2011.7
## - test_prep:transport_means               1    159.71 13571 2012.0
## + gender:ethnic_group                     4     67.22 13344 2012.0
## + parent_educ:writing_score               5    111.91 13299 2012.1
## + parent_educ:reading_score               5    109.78 13302 2012.2
## - is_first_child:wkly_study_hours         2    211.06 13622 2012.2
## + parent_marital_status:writing_score     3     17.14 13394 2012.2
## + parent_marital_status:reading_score     3     16.46 13395 2012.3
## - transport_means:writing_score           1    167.14 13578 2012.3
## + ethnic_group:lunch_type                 4     54.12 13357 2012.6
## + ethnic_group:transport_means            4     43.26 13368 2013.1
## - ethnic_group:is_first_child             4    325.58 13737 2013.2
## + ethnic_group:writing_score              4     32.57 13379 2013.6
## - practice_sport:reading_score            2    249.61 13661 2013.9
## + ethnic_group:reading_score              4     21.46 13390 2014.1
## - lunch_type:is_first_child               1    210.80 13622 2014.2
## - practice_sport:writing_score            2    265.54 13677 2014.6
## + practice_sport:wkly_study_hours         4      4.60 13407 2014.8
## + gender:parent_educ                      5     41.99 13369 2015.2
## + parent_marital_status:wkly_study_hours  6     71.43 13340 2015.8
## + ethnic_group:practice_sport             8    146.02 13265 2016.5
## + ethnic_group:parent_educ               20    669.68 12742 2016.8
## + ethnic_group:parent_marital_status     11    250.32 13161 2017.9
## - is_first_child:transport_means          1    319.62 13731 2018.9
## + parent_educ:practice_sport             10    171.27 13240 2019.4
## + ethnic_group:wkly_study_hours           8     71.34 13340 2019.8
## + parent_educ:wkly_study_hours           10    131.98 13279 2021.2
## + parent_educ:parent_marital_status      15    273.51 13138 2024.8
## 
## Step:  AIC=2005.34
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + transport_means:writing_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:wkly_study_hours              2     53.70 13473 2003.7
## - gender:reading_score                    1     11.36 13430 2003.8
## - gender:test_prep                        1     11.83 13431 2003.9
## - parent_educ:test_prep                   5    203.93 13623 2004.2
## - wkly_study_hours:writing_score          2     69.53 13489 2004.4
## - lunch_type:practice_sport               2     78.84 13498 2004.8
## - lunch_type:wkly_study_hours             2     82.55 13502 2005.0
## - parent_marital_status:practice_sport    6    274.15 13693 2005.3
## <none>                                                13419 2005.3
## - ethnic_group:test_prep                  4    189.08 13608 2005.6
## - gender:writing_score                    1     52.99 13472 2005.7
## - test_prep:parent_marital_status         3    156.45 13576 2006.2
## - is_first_child:writing_score            1     77.51 13497 2006.7
## - writing_score:reading_score             1     78.08 13497 2006.8
## + test_prep:is_first_child                1      7.83 13411 2007.0
## - parent_educ:transport_means             5    272.09 13691 2007.2
## + is_first_child:reading_score            1      2.19 13417 2007.2
## + lunch_type:transport_means              1      1.98 13417 2007.3
## + practice_sport:transport_means          2     47.34 13372 2007.3
## + test_prep:reading_score                 1      1.62 13418 2007.3
## + gender:transport_means                  1      1.46 13418 2007.3
## + transport_means:reading_score           1      1.41 13418 2007.3
## + test_prep:writing_score                 1      0.67 13418 2007.3
## + lunch_type:writing_score                1      0.40 13419 2007.3
## + gender:lunch_type                       1      0.32 13419 2007.3
## + lunch_type:test_prep                    1      0.29 13419 2007.3
## + lunch_type:reading_score                1      0.21 13419 2007.3
## + gender:is_first_child                   1      0.07 13419 2007.3
## + lunch_type:parent_marital_status        2     35.51 13384 2007.8
## + practice_sport:is_first_child           2     23.59 13396 2008.3
## - wkly_study_hours:reading_score          2    160.83 13580 2008.4
## + gender:wkly_study_hours                 2     15.13 13404 2008.7
## + gender:practice_sport                   2     14.92 13404 2008.7
## + transport_means:wkly_study_hours        2     12.60 13406 2008.8
## - parent_educ:is_first_child              5    310.82 13730 2008.8
## + test_prep:practice_sport                2      5.26 13414 2009.1
## + parent_educ:lunch_type                  5    137.40 13282 2009.3
## + gender:parent_marital_status            3     42.03 13377 2009.5
## + parent_marital_status:transport_means   3     38.17 13381 2009.7
## + parent_marital_status:is_first_child    3     30.77 13388 2010.0
## + parent_educ:writing_score               5    115.35 13304 2010.2
## - test_prep:transport_means               1    158.86 13578 2010.3
## + gender:ethnic_group                     4     69.04 13350 2010.3
## + parent_educ:reading_score               5    114.12 13305 2010.3
## - is_first_child:wkly_study_hours         2    209.46 13629 2010.5
## + parent_marital_status:writing_score     3     18.00 13401 2010.5
## + parent_marital_status:reading_score     3     17.45 13402 2010.6
## - transport_means:writing_score           1    171.22 13590 2010.8
## + ethnic_group:lunch_type                 4     52.25 13367 2011.0
## + ethnic_group:transport_means            4     44.71 13374 2011.4
## - ethnic_group:is_first_child             4    324.09 13743 2011.4
## + ethnic_group:writing_score              4     32.98 13386 2011.9
## - lunch_type:is_first_child               1    204.18 13623 2012.2
## - practice_sport:reading_score            2    250.50 13670 2012.3
## + ethnic_group:reading_score              4     21.79 13397 2012.4
## - practice_sport:writing_score            2    267.00 13686 2013.0
## + practice_sport:wkly_study_hours         4      4.44 13415 2013.2
## + gender:parent_educ                      5     44.41 13375 2013.4
## + parent_marital_status:wkly_study_hours  6     69.62 13350 2014.3
## + ethnic_group:parent_educ               20    675.36 12744 2014.9
## + ethnic_group:practice_sport             8    144.87 13274 2014.9
## + ethnic_group:parent_marital_status     11    257.17 13162 2015.9
## - is_first_child:transport_means          1    324.75 13744 2017.5
## + parent_educ:practice_sport             10    171.99 13247 2017.7
## + ethnic_group:wkly_study_hours           8     75.50 13344 2018.0
## + parent_educ:wkly_study_hours           10    133.41 13286 2019.5
## + parent_educ:parent_marital_status      15    274.03 13145 2023.2
## 
## Step:  AIC=2003.7
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:transport_means + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - wkly_study_hours:writing_score          2     37.33 13510 2001.3
## - gender:reading_score                    1     12.37 13485 2002.2
## - gender:test_prep                        1     13.16 13486 2002.3
## - parent_educ:test_prep                   5    205.40 13678 2002.6
## - lunch_type:practice_sport               2     76.12 13549 2003.0
## - parent_marital_status:practice_sport    6    267.68 13740 2003.3
## <none>                                                13473 2003.7
## - ethnic_group:test_prep                  4    185.25 13658 2003.8
## - lunch_type:wkly_study_hours             2     93.74 13567 2003.8
## - gender:writing_score                    1     53.84 13527 2004.0
## - test_prep:parent_marital_status         3    152.18 13625 2004.3
## - parent_educ:transport_means             5    256.86 13730 2004.8
## - wkly_study_hours:reading_score          2    120.72 13594 2005.0
## - is_first_child:writing_score            1     75.79 13549 2005.0
## - writing_score:reading_score             1     79.19 13552 2005.2
## + test_prep:wkly_study_hours              2     53.70 13419 2005.3
## + test_prep:is_first_child                1      6.41 13466 2005.4
## + lunch_type:transport_means              1      5.29 13468 2005.5
## + test_prep:reading_score                 1      3.13 13470 2005.6
## + practice_sport:transport_means          2     47.51 13425 2005.6
## + test_prep:writing_score                 1      1.72 13471 2005.6
## + is_first_child:reading_score            1      0.86 13472 2005.7
## + lunch_type:test_prep                    1      0.75 13472 2005.7
## + gender:lunch_type                       1      0.72 13472 2005.7
## + lunch_type:writing_score                1      0.70 13472 2005.7
## + gender:transport_means                  1      0.52 13472 2005.7
## + transport_means:reading_score           1      0.51 13472 2005.7
## + lunch_type:reading_score                1      0.35 13472 2005.7
## + gender:is_first_child                   1      0.19 13473 2005.7
## + lunch_type:parent_marital_status        2     33.50 13439 2006.2
## - parent_educ:is_first_child              5    295.29 13768 2006.5
## + gender:wkly_study_hours                 2     24.87 13448 2006.6
## + practice_sport:is_first_child           2     24.03 13449 2006.7
## + gender:practice_sport                   2     16.24 13457 2007.0
## + transport_means:wkly_study_hours        2      9.09 13464 2007.3
## + test_prep:practice_sport                2      4.99 13468 2007.5
## + parent_educ:lunch_type                  5    137.81 13335 2007.6
## + gender:parent_marital_status            3     45.44 13427 2007.7
## + parent_marital_status:is_first_child    3     34.52 13438 2008.2
## + parent_marital_status:transport_means   3     33.67 13439 2008.2
## - is_first_child:wkly_study_hours         2    201.89 13675 2008.5
## + parent_educ:reading_score               5    118.46 13354 2008.5
## + gender:ethnic_group                     4     69.97 13403 2008.6
## - transport_means:writing_score           1    159.47 13632 2008.6
## + parent_educ:writing_score               5    114.34 13358 2008.7
## + parent_marital_status:reading_score     3     21.62 13451 2008.8
## - test_prep:transport_means               1    162.03 13635 2008.8
## + parent_marital_status:writing_score     3     21.04 13452 2008.8
## - ethnic_group:is_first_child             4    306.48 13779 2009.0
## + ethnic_group:lunch_type                 4     58.44 13414 2009.1
## + ethnic_group:transport_means            4     45.26 13428 2009.7
## + ethnic_group:writing_score              4     35.20 13438 2010.2
## - practice_sport:reading_score            2    243.69 13716 2010.3
## + ethnic_group:reading_score              4     22.35 13450 2010.7
## - lunch_type:is_first_child               1    209.54 13682 2010.8
## - practice_sport:writing_score            2    264.96 13738 2011.2
## + practice_sport:wkly_study_hours         4      2.31 13470 2011.6
## + gender:parent_educ                      5     46.05 13427 2011.7
## + parent_marital_status:wkly_study_hours  6     64.09 13409 2012.9
## + ethnic_group:parent_educ               20    684.31 12788 2013.0
## + ethnic_group:practice_sport             8    143.72 13329 2013.4
## + ethnic_group:parent_marital_status     11    257.93 13215 2014.3
## - is_first_child:transport_means          1    313.76 13787 2015.3
## + ethnic_group:wkly_study_hours           8     90.98 13382 2015.7
## + parent_educ:practice_sport             10    156.88 13316 2016.8
## + parent_educ:wkly_study_hours           10    115.35 13358 2018.6
## + parent_educ:parent_marital_status      15    286.40 13186 2021.0
## 
## Step:  AIC=2001.33
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:test_prep + gender:writing_score + gender:reading_score + 
##     ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:transport_means + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:test_prep                        1     13.42 13524 1999.9
## - gender:reading_score                    1     13.79 13524 1999.9
## - parent_educ:test_prep                   5    204.00 13714 2000.2
## - lunch_type:practice_sport               2     80.06 13590 2000.8
## - parent_marital_status:practice_sport    6    273.14 13783 2001.1
## <none>                                                13510 2001.3
## - lunch_type:wkly_study_hours             2     96.48 13607 2001.5
## - test_prep:parent_marital_status         3    145.52 13656 2001.7
## - gender:writing_score                    1     57.21 13567 2001.8
## - ethnic_group:test_prep                  4    201.87 13712 2002.1
## - is_first_child:writing_score            1     75.66 13586 2002.6
## - parent_educ:transport_means             5    265.29 13775 2002.8
## - writing_score:reading_score             1     80.66 13591 2002.8
## + test_prep:is_first_child                1      7.12 13503 2003.0
## + lunch_type:transport_means              1      6.06 13504 2003.1
## + test_prep:reading_score                 1      3.86 13506 2003.2
## + test_prep:writing_score                 1      1.90 13508 2003.2
## + gender:lunch_type                       1      1.63 13508 2003.3
## + lunch_type:writing_score                1      1.57 13509 2003.3
## + lunch_type:test_prep                    1      0.82 13509 2003.3
## + lunch_type:reading_score                1      0.79 13509 2003.3
## + is_first_child:reading_score            1      0.64 13510 2003.3
## + practice_sport:transport_means          2     46.12 13464 2003.3
## + gender:transport_means                  1      0.31 13510 2003.3
## + transport_means:reading_score           1      0.17 13510 2003.3
## + gender:is_first_child                   1      0.00 13510 2003.3
## + wkly_study_hours:writing_score          2     37.33 13473 2003.7
## - parent_educ:is_first_child              5    286.46 13797 2003.7
## + gender:wkly_study_hours                 2     35.87 13474 2003.8
## + lunch_type:parent_marital_status        2     34.32 13476 2003.8
## + practice_sport:is_first_child           2     22.39 13488 2004.3
## + test_prep:wkly_study_hours              2     21.49 13489 2004.4
## + gender:practice_sport                   2     18.48 13492 2004.5
## + transport_means:wkly_study_hours        2     10.34 13500 2004.9
## + test_prep:practice_sport                2      4.56 13506 2005.1
## + gender:parent_marital_status            3     42.69 13467 2005.5
## + parent_educ:lunch_type                  5    133.25 13377 2005.5
## - is_first_child:wkly_study_hours         2    192.78 13703 2005.7
## + parent_marital_status:transport_means   3     36.80 13473 2005.7
## + parent_marital_status:is_first_child    3     35.50 13475 2005.8
## + parent_educ:reading_score               5    121.18 13389 2006.0
## + parent_educ:writing_score               5    118.16 13392 2006.2
## + gender:ethnic_group                     4     70.08 13440 2006.3
## + parent_marital_status:writing_score     3     23.68 13486 2006.3
## + parent_marital_status:reading_score     3     23.57 13487 2006.3
## - transport_means:writing_score           1    162.52 13673 2006.4
## - test_prep:transport_means               1    162.53 13673 2006.4
## - ethnic_group:is_first_child             4    307.86 13818 2006.6
## + ethnic_group:lunch_type                 4     49.27 13461 2007.2
## + ethnic_group:transport_means            4     48.14 13462 2007.2
## - practice_sport:reading_score            2    233.87 13744 2007.5
## + ethnic_group:writing_score              4     36.19 13474 2007.8
## - lunch_type:is_first_child               1    198.77 13709 2008.0
## + ethnic_group:reading_score              4     23.65 13486 2008.3
## - practice_sport:writing_score            2    256.94 13767 2008.5
## + practice_sport:wkly_study_hours         4      5.64 13504 2009.1
## + gender:parent_educ                      5     48.27 13462 2009.2
## - wkly_study_hours:reading_score          2    291.10 13801 2009.9
## + ethnic_group:parent_educ               20    689.47 12821 2010.4
## + parent_marital_status:wkly_study_hours  6     55.21 13455 2010.9
## + ethnic_group:practice_sport             8    141.71 13368 2011.1
## + ethnic_group:parent_marital_status     11    257.26 13253 2012.0
## - is_first_child:transport_means          1    309.34 13820 2012.7
## + ethnic_group:wkly_study_hours           8     94.09 13416 2013.2
## + parent_educ:practice_sport             10    159.61 13350 2014.3
## + parent_educ:wkly_study_hours           10    122.06 13388 2016.0
## + parent_educ:parent_marital_status      15    275.73 13234 2019.2
## 
## Step:  AIC=1999.92
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:writing_score + gender:reading_score + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + parent_educ:test_prep + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:transport_means + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:reading_score                    1      8.80 13532 1998.3
## - parent_educ:test_prep                   5    203.39 13727 1998.7
## - lunch_type:practice_sport               2     77.92 13602 1999.3
## - parent_marital_status:practice_sport    6    272.75 13796 1999.7
## <none>                                                13524 1999.9
## - gender:writing_score                    1     45.96 13570 1999.9
## - lunch_type:wkly_study_hours             2     98.25 13622 2000.2
## - test_prep:parent_marital_status         3    146.11 13670 2000.3
## - ethnic_group:test_prep                  4    202.57 13726 2000.7
## - parent_educ:transport_means             5    255.28 13779 2001.0
## - is_first_child:writing_score            1     71.14 13595 2001.0
## + gender:test_prep                        1     13.42 13510 2001.3
## - writing_score:reading_score             1     82.43 13606 2001.5
## + test_prep:is_first_child                1      7.53 13516 2001.6
## + lunch_type:transport_means              1      5.45 13518 2001.7
## + gender:lunch_type                       1      3.10 13520 2001.8
## + practice_sport:transport_means          2     48.27 13475 2001.8
## + lunch_type:writing_score                1      2.09 13522 2001.8
## + lunch_type:reading_score                1      1.20 13522 2001.9
## + lunch_type:test_prep                    1      1.17 13522 2001.9
## + gender:transport_means                  1      0.72 13523 2001.9
## + test_prep:reading_score                 1      0.64 13523 2001.9
## + transport_means:reading_score           1      0.41 13523 2001.9
## + is_first_child:reading_score            1      0.33 13523 2001.9
## + gender:is_first_child                   1      0.05 13524 2001.9
## + test_prep:writing_score                 1      0.00 13524 2001.9
## + gender:wkly_study_hours                 2     38.76 13485 2002.2
## + wkly_study_hours:writing_score          2     37.59 13486 2002.3
## - parent_educ:is_first_child              5    290.36 13814 2002.5
## + lunch_type:parent_marital_status        2     31.99 13492 2002.5
## + test_prep:wkly_study_hours              2     22.59 13501 2002.9
## + practice_sport:is_first_child           2     21.63 13502 2003.0
## + gender:practice_sport                   2     17.88 13506 2003.1
## + transport_means:wkly_study_hours        2     10.30 13513 2003.5
## + test_prep:practice_sport                2      4.74 13519 2003.7
## + gender:parent_marital_status            3     41.84 13482 2004.1
## - is_first_child:wkly_study_hours         2    189.66 13713 2004.1
## + parent_educ:lunch_type                  5    127.40 13396 2004.3
## + parent_marital_status:transport_means   3     35.70 13488 2004.4
## + parent_marital_status:is_first_child    3     34.22 13489 2004.4
## - transport_means:writing_score           1    153.56 13677 2004.6
## + gender:ethnic_group                     4     76.21 13447 2004.6
## - test_prep:transport_means               1    155.98 13680 2004.7
## + parent_educ:reading_score               5    118.40 13405 2004.7
## + parent_marital_status:writing_score     3     25.19 13498 2004.8
## + parent_marital_status:reading_score     3     24.25 13499 2004.9
## + parent_educ:writing_score               5    113.87 13410 2004.9
## - ethnic_group:is_first_child             4    309.93 13834 2005.3
## + ethnic_group:transport_means            4     50.94 13473 2005.7
## + ethnic_group:lunch_type                 4     50.63 13473 2005.7
## - practice_sport:reading_score            2    231.35 13755 2005.9
## + ethnic_group:writing_score              4     41.24 13482 2006.1
## - lunch_type:is_first_child               1    195.18 13719 2006.4
## + ethnic_group:reading_score              4     27.18 13496 2006.7
## - practice_sport:writing_score            2    254.99 13779 2006.9
## + practice_sport:wkly_study_hours         4      6.13 13517 2007.7
## + gender:parent_educ                      5     48.86 13475 2007.8
## + ethnic_group:parent_educ               20    700.93 12823 2008.5
## - wkly_study_hours:reading_score          2    294.58 13818 2008.6
## + parent_marital_status:wkly_study_hours  6     52.60 13471 2009.6
## + ethnic_group:practice_sport             8    139.38 13384 2009.8
## + ethnic_group:parent_marital_status     11    255.23 13268 2010.7
## - is_first_child:transport_means          1    312.53 13836 2011.4
## + ethnic_group:wkly_study_hours           8     95.89 13428 2011.7
## + parent_educ:practice_sport             10    154.00 13370 2013.2
## + parent_educ:wkly_study_hours           10    122.43 13401 2014.5
## + parent_educ:parent_marital_status      15    276.17 13247 2017.8
## 
## Step:  AIC=1998.3
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:writing_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:transport_means + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:test_prep                   5    201.80 13734 1997.0
## - lunch_type:practice_sport               2     78.51 13611 1997.7
## <none>                                                13532 1998.3
## - test_prep:parent_marital_status         3    144.92 13677 1998.6
## - parent_marital_status:practice_sport    6    291.83 13824 1998.9
## - lunch_type:wkly_study_hours             2    107.76 13640 1999.0
## - parent_educ:transport_means             5    247.50 13780 1999.0
## - ethnic_group:test_prep                  4    204.35 13737 1999.2
## - is_first_child:writing_score            1     72.61 13605 1999.5
## - writing_score:reading_score             1     79.38 13612 1999.8
## + gender:reading_score                    1      8.80 13524 1999.9
## + gender:test_prep                        1      8.43 13524 1999.9
## + test_prep:is_first_child                1      7.75 13525 2000.0
## + lunch_type:transport_means              1      5.48 13527 2000.1
## + practice_sport:transport_means          2     50.70 13482 2000.1
## + gender:lunch_type                       1      3.10 13529 2000.2
## + lunch_type:writing_score                1      2.53 13530 2000.2
## + lunch_type:reading_score                1      1.58 13531 2000.2
## + lunch_type:test_prep                    1      1.45 13531 2000.2
## + test_prep:reading_score                 1      1.43 13531 2000.2
## + transport_means:reading_score           1      0.62 13532 2000.3
## + gender:transport_means                  1      0.56 13532 2000.3
## + test_prep:writing_score                 1      0.22 13532 2000.3
## + gender:is_first_child                   1      0.10 13532 2000.3
## + is_first_child:reading_score            1      0.08 13532 2000.3
## + gender:wkly_study_hours                 2     38.91 13494 2000.6
## + wkly_study_hours:writing_score          2     38.70 13494 2000.6
## + lunch_type:parent_marital_status        2     33.64 13499 2000.8
## - parent_educ:is_first_child              5    291.98 13824 2000.9
## + test_prep:wkly_study_hours              2     23.07 13509 2001.3
## + practice_sport:is_first_child           2     21.18 13511 2001.4
## + gender:practice_sport                   2     14.72 13518 2001.7
## + transport_means:wkly_study_hours        2     11.73 13521 2001.8
## + test_prep:practice_sport                2      5.03 13527 2002.1
## - is_first_child:wkly_study_hours         2    191.44 13724 2002.6
## + parent_educ:lunch_type                  5    130.19 13402 2002.6
## + gender:parent_marital_status            3     38.58 13494 2002.6
## + parent_marital_status:transport_means   3     37.22 13495 2002.7
## + gender:ethnic_group                     4     81.97 13450 2002.7
## + parent_marital_status:is_first_child    3     31.57 13501 2002.9
## - transport_means:writing_score           1    153.39 13686 2003.0
## - test_prep:transport_means               1    156.01 13688 2003.1
## + parent_marital_status:writing_score     3     27.13 13505 2003.1
## + parent_marital_status:reading_score     3     25.08 13507 2003.2
## + parent_educ:reading_score               5    114.38 13418 2003.3
## + parent_educ:writing_score               5    110.43 13422 2003.5
## - ethnic_group:is_first_child             4    306.80 13839 2003.5
## - gender:writing_score                    1    175.84 13708 2003.9
## + ethnic_group:transport_means            4     52.24 13480 2004.0
## + ethnic_group:lunch_type                 4     50.55 13482 2004.1
## - practice_sport:reading_score            2    232.38 13765 2004.3
## + ethnic_group:writing_score              4     40.00 13492 2004.6
## - lunch_type:is_first_child               1    197.44 13730 2004.8
## + ethnic_group:reading_score              4     25.49 13507 2005.2
## - practice_sport:writing_score            2    255.78 13788 2005.3
## + practice_sport:wkly_study_hours         4      5.43 13527 2006.1
## + gender:parent_educ                      5     49.96 13482 2006.1
## + ethnic_group:parent_educ               20    697.47 12835 2007.1
## - wkly_study_hours:reading_score          2    298.82 13831 2007.2
## + parent_marital_status:wkly_study_hours  6     54.12 13478 2007.9
## + ethnic_group:practice_sport             8    138.17 13394 2008.2
## + ethnic_group:parent_marital_status     11    248.39 13284 2009.4
## + ethnic_group:wkly_study_hours           8     92.34 13440 2010.3
## - is_first_child:transport_means          1    326.26 13859 2010.4
## + parent_educ:practice_sport             10    141.55 13391 2012.1
## + parent_educ:wkly_study_hours           10    121.33 13411 2013.0
## + parent_educ:parent_marital_status      15    271.46 13261 2016.3
## 
## Step:  AIC=1997.04
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:writing_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:transport_means + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:practice_sport               2     86.65 13821 1996.8
## <none>                                                13734 1997.0
## - test_prep:parent_marital_status         3    142.87 13877 1997.1
## - parent_educ:transport_means             5    239.49 13974 1997.2
## - parent_marital_status:practice_sport    6    300.39 14034 1997.8
## - ethnic_group:test_prep                  4    211.45 13946 1998.0
## + practice_sport:transport_means          2     63.88 13670 1998.3
## + parent_educ:test_prep                   5    201.80 13532 1998.3
## - lunch_type:wkly_study_hours             2    125.52 13860 1998.4
## - is_first_child:writing_score            1     78.87 13813 1998.4
## - writing_score:reading_score             1     82.05 13816 1998.5
## + lunch_type:transport_means              1      8.74 13725 1998.7
## + test_prep:is_first_child                1      8.47 13726 1998.7
## + gender:test_prep                        1      8.38 13726 1998.7
## + gender:reading_score                    1      7.21 13727 1998.7
## + lunch_type:writing_score                1      1.96 13732 1999.0
## + gender:lunch_type                       1      1.34 13733 1999.0
## + lunch_type:reading_score                1      1.24 13733 1999.0
## + gender:transport_means                  1      0.74 13733 1999.0
## + transport_means:reading_score           1      0.56 13734 1999.0
## + lunch_type:test_prep                    1      0.56 13734 1999.0
## + test_prep:reading_score                 1      0.22 13734 1999.0
## + gender:is_first_child                   1      0.20 13734 1999.0
## + is_first_child:reading_score            1      0.14 13734 1999.0
## + test_prep:writing_score                 1      0.00 13734 1999.0
## - parent_educ:is_first_child              5    285.05 14019 1999.2
## + wkly_study_hours:writing_score          2     36.95 13697 1999.5
## + gender:wkly_study_hours                 2     35.80 13698 1999.5
## + lunch_type:parent_marital_status        2     35.79 13698 1999.5
## + practice_sport:is_first_child           2     35.32 13699 1999.5
## + test_prep:wkly_study_hours              2     23.19 13711 2000.0
## - is_first_child:wkly_study_hours         2    166.44 13901 2000.1
## + gender:practice_sport                   2     18.54 13716 2000.2
## + transport_means:wkly_study_hours        2      9.96 13724 2000.6
## + test_prep:practice_sport                2      3.44 13731 2000.9
## - test_prep:transport_means               1    136.91 13871 2000.9
## - transport_means:writing_score           1    139.08 13873 2001.0
## + parent_educ:lunch_type                  5    136.82 13597 2001.1
## + parent_marital_status:transport_means   3     43.64 13690 2001.2
## + gender:ethnic_group                     4     89.08 13645 2001.2
## + parent_marital_status:is_first_child    3     34.73 13699 2001.5
## + parent_marital_status:writing_score     3     29.78 13704 2001.8
## + parent_marital_status:reading_score     3     29.17 13705 2001.8
## + parent_educ:reading_score               5    118.65 13616 2001.9
## + gender:parent_marital_status            3     25.24 13709 2002.0
## - practice_sport:reading_score            2    211.32 13946 2002.0
## - ethnic_group:is_first_child             4    309.13 14043 2002.2
## - gender:writing_score                    1    170.68 13905 2002.3
## + parent_educ:writing_score               5    108.51 13626 2002.4
## + ethnic_group:lunch_type                 4     53.25 13681 2002.7
## + ethnic_group:transport_means            4     50.59 13684 2002.9
## - practice_sport:writing_score            2    234.46 13969 2003.0
## + ethnic_group:writing_score              4     33.63 13700 2003.6
## + ethnic_group:reading_score              4     23.00 13711 2004.0
## - lunch_type:is_first_child               1    226.97 13961 2004.7
## + practice_sport:wkly_study_hours         4      3.68 13730 2004.9
## + gender:parent_educ                      5     42.30 13692 2005.2
## + ethnic_group:parent_educ               20    716.59 13018 2005.4
## - wkly_study_hours:reading_score          2    302.92 14037 2005.9
## + parent_marital_status:wkly_study_hours  6     59.55 13675 2006.5
## + ethnic_group:practice_sport             8    141.57 13593 2006.9
## + ethnic_group:wkly_study_hours           8     92.03 13642 2009.1
## - is_first_child:transport_means          1    337.16 14071 2009.3
## + ethnic_group:parent_marital_status     11    210.71 13523 2009.9
## + parent_educ:practice_sport             10    128.28 13606 2011.5
## + parent_educ:wkly_study_hours           10    122.34 13612 2011.8
## + parent_educ:parent_marital_status      15    268.36 13466 2015.4
## 
## Step:  AIC=1996.75
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:writing_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:transport_means + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:transport_means             5    232.30 14053 1996.6
## <none>                                                13821 1996.8
## - parent_marital_status:practice_sport    6    286.41 14107 1996.8
## + lunch_type:practice_sport               2     86.65 13734 1997.0
## - test_prep:parent_marital_status         3    159.55 13980 1997.5
## + parent_educ:test_prep                   5    209.94 13611 1997.7
## + practice_sport:transport_means          2     69.40 13751 1997.8
## - lunch_type:wkly_study_hours             2    122.61 13943 1998.0
## - ethnic_group:test_prep                  4    218.41 14039 1998.0
## - writing_score:reading_score             1     81.91 13903 1998.2
## + test_prep:is_first_child                1     10.45 13810 1998.3
## - is_first_child:writing_score            1     84.28 13905 1998.3
## + gender:reading_score                    1      7.80 13813 1998.4
## + gender:test_prep                        1      6.36 13814 1998.5
## - parent_educ:is_first_child              5    277.57 14098 1998.5
## + lunch_type:transport_means              1      6.00 13815 1998.5
## + gender:is_first_child                   1      3.02 13818 1998.6
## + lunch_type:writing_score                1      2.15 13819 1998.7
## + lunch_type:test_prep                    1      1.01 13820 1998.7
## + lunch_type:reading_score                1      0.77 13820 1998.7
## + transport_means:reading_score           1      0.67 13820 1998.7
## + gender:lunch_type                       1      0.62 13820 1998.7
## + gender:transport_means                  1      0.48 13820 1998.7
## + is_first_child:reading_score            1      0.29 13820 1998.7
## + test_prep:reading_score                 1      0.23 13821 1998.7
## + test_prep:writing_score                 1      0.08 13821 1998.7
## + lunch_type:parent_marital_status        2     43.71 13777 1998.9
## + gender:wkly_study_hours                 2     43.19 13778 1998.9
## + wkly_study_hours:writing_score          2     40.97 13780 1999.0
## + practice_sport:is_first_child           2     37.68 13783 1999.1
## + test_prep:wkly_study_hours              2     20.94 13800 1999.8
## + gender:practice_sport                   2     13.89 13807 2000.2
## + transport_means:wkly_study_hours        2     10.28 13810 2000.3
## - transport_means:writing_score           1    132.58 13953 2000.4
## - is_first_child:wkly_study_hours         2    180.30 14001 2000.4
## + test_prep:practice_sport                2      7.16 13814 2000.4
## - test_prep:transport_means               1    134.58 13955 2000.5
## + gender:ethnic_group                     4     95.29 13726 2000.7
## + parent_marital_status:transport_means   3     46.82 13774 2000.7
## - ethnic_group:is_first_child             4    288.87 14110 2001.0
## + parent_marital_status:writing_score     3     41.82 13779 2001.0
## + parent_marital_status:reading_score     3     41.64 13779 2001.0
## - practice_sport:reading_score            2    195.51 14016 2001.0
## + parent_educ:reading_score               5    131.60 13689 2001.1
## + parent_educ:lunch_type                  5    121.16 13700 2001.5
## + parent_marital_status:is_first_child    3     25.35 13796 2001.7
## + parent_educ:writing_score               5    117.74 13703 2001.7
## + gender:parent_marital_status            3     22.11 13799 2001.8
## + ethnic_group:transport_means            4     63.16 13758 2002.0
## - practice_sport:writing_score            2    220.63 14041 2002.1
## - gender:writing_score                    1    175.20 13996 2002.2
## + ethnic_group:lunch_type                 4     44.01 13777 2002.9
## - lunch_type:is_first_child               1    197.04 14018 2003.1
## + ethnic_group:writing_score              4     26.52 13794 2003.6
## + ethnic_group:reading_score              4     17.79 13803 2004.0
## + practice_sport:wkly_study_hours         4      2.00 13819 2004.7
## + gender:parent_educ                      5     47.40 13773 2004.7
## - wkly_study_hours:reading_score          2    286.88 14108 2004.9
## + parent_marital_status:wkly_study_hours  6     56.23 13765 2006.3
## + ethnic_group:parent_educ               20    692.34 13128 2006.4
## + ethnic_group:practice_sport             8    143.83 13677 2006.6
## + ethnic_group:wkly_study_hours           8     89.30 13732 2008.9
## + ethnic_group:parent_marital_status     11    224.89 13596 2009.1
## - is_first_child:transport_means          1    353.37 14174 2009.6
## + parent_educ:practice_sport             10    130.21 13691 2011.2
## + parent_educ:wkly_study_hours           10    121.53 13699 2011.5
## + parent_educ:parent_marital_status      15    272.23 13549 2015.0
## 
## Step:  AIC=1996.58
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + reading_score + 
##     gender:writing_score + ethnic_group:test_prep + ethnic_group:is_first_child + 
##     parent_educ:is_first_child + lunch_type:is_first_child + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:transport_means + parent_marital_status:practice_sport + 
##     practice_sport:writing_score + practice_sport:reading_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + transport_means:writing_score + 
##     wkly_study_hours:reading_score + writing_score:reading_score
## 
##                                          Df Sum of Sq   RSS    AIC
## <none>                                                14053 1996.6
## - parent_educ:is_first_child              5    243.00 14296 1996.7
## + parent_educ:transport_means             5    232.30 13821 1996.8
## + lunch_type:practice_sport               2     79.45 13974 1997.2
## - parent_marital_status:practice_sport    6    309.19 14362 1997.4
## - test_prep:parent_marital_status         3    164.69 14218 1997.5
## - transport_means:writing_score           1     71.84 14125 1997.6
## - lunch_type:wkly_study_hours             2    120.40 14174 1997.6
## + test_prep:is_first_child                1     15.23 14038 1997.9
## - is_first_child:writing_score            1     80.30 14133 1997.9
## - writing_score:reading_score             1     82.81 14136 1998.0
## + parent_educ:test_prep                   5    199.75 13853 1998.1
## + transport_means:reading_score           1      6.93 14046 1998.3
## + lunch_type:test_prep                    1      3.36 14050 1998.4
## + lunch_type:writing_score                1      3.17 14050 1998.5
## + gender:wkly_study_hours                 2     50.20 14003 1998.5
## + gender:is_first_child                   1      2.46 14051 1998.5
## + gender:test_prep                        1      2.33 14051 1998.5
## + wkly_study_hours:writing_score          2     49.45 14004 1998.5
## + lunch_type:reading_score                1      1.51 14052 1998.5
## + gender:transport_means                  1      1.34 14052 1998.5
## + is_first_child:reading_score            1      0.90 14052 1998.5
## + gender:lunch_type                       1      0.73 14052 1998.5
## + practice_sport:transport_means          2     48.17 14005 1998.6
## + gender:reading_score                    1      0.54 14053 1998.6
## + test_prep:reading_score                 1      0.41 14053 1998.6
## + lunch_type:transport_means              1      0.09 14053 1998.6
## + test_prep:writing_score                 1      0.06 14053 1998.6
## + practice_sport:is_first_child           2     44.89 14008 1998.7
## - ethnic_group:test_prep                  4    244.53 14298 1998.8
## + lunch_type:parent_marital_status        2     40.32 14013 1998.9
## - is_first_child:wkly_study_hours         2    159.16 14212 1999.2
## + test_prep:wkly_study_hours              2     13.46 14040 2000.0
## + parent_marital_status:reading_score     3     58.75 13994 2000.1
## - practice_sport:reading_score            2    182.63 14236 2000.2
## + gender:practice_sport                   2      8.44 14045 2000.2
## + test_prep:practice_sport                2      5.82 14047 2000.3
## + transport_means:wkly_study_hours        2      5.20 14048 2000.4
## + parent_marital_status:writing_score     3     51.35 14002 2000.4
## - test_prep:transport_means               1    142.53 14196 2000.5
## + parent_marital_status:transport_means   3     41.68 14011 2000.8
## - ethnic_group:is_first_child             4    297.56 14351 2000.9
## + parent_marital_status:is_first_child    3     37.25 14016 2001.0
## + parent_educ:reading_score               5    129.71 13923 2001.1
## + gender:ethnic_group                     4     82.34 13971 2001.1
## + gender:parent_marital_status            3     27.68 14025 2001.4
## - practice_sport:writing_score            2    215.10 14268 2001.5
## + parent_educ:lunch_type                  5    117.82 13935 2001.6
## + parent_educ:writing_score               5    112.10 13941 2001.9
## - gender:writing_score                    1    182.12 14235 2002.2
## - lunch_type:is_first_child               1    186.60 14240 2002.4
## + ethnic_group:transport_means            4     51.34 14002 2002.4
## + ethnic_group:lunch_type                 4     44.73 14008 2002.7
## + ethnic_group:writing_score              4     30.89 14022 2003.3
## + ethnic_group:reading_score              4     18.88 14034 2003.8
## - wkly_study_hours:reading_score          2    277.37 14330 2004.1
## + practice_sport:wkly_study_hours         4      7.28 14046 2004.3
## + gender:parent_educ                      5     49.63 14004 2004.5
## + ethnic_group:parent_educ               20    721.15 13332 2005.5
## + parent_marital_status:wkly_study_hours  6     65.25 13988 2005.8
## + ethnic_group:practice_sport             8    153.25 13900 2006.1
## + ethnic_group:parent_marital_status     11    262.78 13790 2007.4
## + ethnic_group:wkly_study_hours           8     81.47 13972 2009.2
## - is_first_child:transport_means          1    384.88 14438 2010.5
## + parent_educ:practice_sport             10    135.76 13917 2010.8
## + parent_educ:wkly_study_hours           10    116.54 13937 2011.7
## + parent_educ:parent_marital_status      15    276.02 13777 2014.9
summary(stepwise_model_math2)
## 
## Call:
## lm(formula = math_score ~ gender + ethnic_group + parent_educ + 
##     lunch_type + test_prep + parent_marital_status + practice_sport + 
##     is_first_child + transport_means + wkly_study_hours + writing_score + 
##     reading_score + gender:writing_score + ethnic_group:test_prep + 
##     ethnic_group:is_first_child + parent_educ:is_first_child + 
##     lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:transport_means + 
##     parent_marital_status:practice_sport + practice_sport:writing_score + 
##     practice_sport:reading_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:reading_score + 
##     writing_score:reading_score, data = df_4_mdl_math2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.2205  -3.1685   0.1617   3.0255  14.1753 
## 
## Coefficients:
##                                                        Estimate Std. Error
## (Intercept)                                          -3.7732346  6.1060153
## gendermale                                           19.5037678  2.1350965
## ethnic_groupgroup B                                   0.0911814  1.9626266
## ethnic_groupgroup C                                   2.2583221  1.9063393
## ethnic_groupgroup D                                  -2.3065390  1.9766142
## ethnic_groupgroup E                                   6.8721719  2.0811662
## parent_educbachelor's degree                          0.7246770  1.3336275
## parent_educhigh school                               -0.0376461  1.2401768
## parent_educmaster's degree                           -5.6191979  1.9393807
## parent_educsome college                               0.2438043  1.2155068
## parent_educsome high school                           1.5300633  1.2215785
## lunch_typestandard                                    2.5885838  1.1720655
## test_prepnone                                         1.4634745  1.9994107
## parent_marital_statusmarried                         -3.9453199  1.8544617
## parent_marital_statussingle                          -7.0721210  2.3632601
## parent_marital_statuswidowed                          2.3207244  3.6534230
## practice_sportregularly                              -3.4108699  4.2307260
## practice_sportsometimes                              -3.8354109  4.1741735
## is_first_childyes                                    -0.9346879  3.0610929
## transport_meansschool_bus                             6.8492626  2.4855490
## wkly_study_hours> 10                                 -6.5941563  3.1856983
## wkly_study_hours10-May                               -1.6692567  2.5757555
## writing_score                                         0.3703874  0.1581504
## reading_score                                         0.3645115  0.1585190
## gendermale:writing_score                             -0.0801567  0.0306717
## ethnic_groupgroup B:test_prepnone                    -0.0531441  1.8722180
## ethnic_groupgroup C:test_prepnone                    -0.0459041  1.7949174
## ethnic_groupgroup D:test_prepnone                     3.2520088  1.8564117
## ethnic_groupgroup E:test_prepnone                    -0.2413349  1.9584231
## ethnic_groupgroup B:is_first_childyes                 1.2077538  1.9099819
## ethnic_groupgroup C:is_first_childyes                -3.2494575  1.8175354
## ethnic_groupgroup D:is_first_childyes                -0.7330669  1.8397464
## ethnic_groupgroup E:is_first_childyes                -1.7216009  2.0704415
## parent_educbachelor's degree:is_first_childyes       -2.8682520  1.6564331
## parent_educhigh school:is_first_childyes              1.0411100  1.5060373
## parent_educmaster's degree:is_first_childyes          3.3535434  2.2486132
## parent_educsome college:is_first_childyes            -0.6354479  1.4852010
## parent_educsome high school:is_first_childyes        -0.7064389  1.4850533
## lunch_typestandard:is_first_childyes                  2.7993264  1.0582225
## lunch_typestandard:wkly_study_hours> 10              -3.1990455  1.5057795
## lunch_typestandard:wkly_study_hours10-May            -1.2823329  1.1408100
## test_prepnone:parent_marital_statusmarried            3.1877010  1.3277750
## test_prepnone:parent_marital_statussingle             3.1318541  1.4967208
## test_prepnone:parent_marital_statuswidowed            1.6334414  3.8228684
## test_prepnone:transport_meansschool_bus              -2.2970524  0.9935766
## parent_marital_statusmarried:practice_sportregularly  3.4752009  1.9447658
## parent_marital_statussingle:practice_sportregularly   7.0869988  2.4423040
## parent_marital_statuswidowed:practice_sportregularly -2.8100117  4.9287326
## parent_marital_statusmarried:practice_sportsometimes  2.6438159  1.8543985
## parent_marital_statussingle:practice_sportsometimes   4.8775517  2.3549791
## parent_marital_statuswidowed:practice_sportsometimes -0.0954158  5.2650211
## practice_sportregularly:writing_score                 0.3133280  0.1690612
## practice_sportsometimes:writing_score                 0.4517201  0.1619272
## practice_sportregularly:reading_score                -0.2969884  0.1667680
## practice_sportsometimes:reading_score                -0.4161670  0.1602656
## is_first_childyes:transport_meansschool_bus          -3.7791725  0.9947473
## is_first_childyes:wkly_study_hours> 10                0.8035222  1.4523725
## is_first_childyes:wkly_study_hours10-May             -2.0145800  1.1318191
## is_first_childyes:writing_score                       0.0596601  0.0343793
## transport_meansschool_bus:writing_score              -0.0500286  0.0304807
## wkly_study_hours> 10:reading_score                    0.1510529  0.0470513
## wkly_study_hours10-May:reading_score                  0.0722752  0.0366033
## writing_score:reading_score                           0.0013020  0.0007388
##                                                      t value Pr(>|t|)    
## (Intercept)                                           -0.618 0.536873    
## gendermale                                             9.135  < 2e-16 ***
## ethnic_groupgroup B                                    0.046 0.962962    
## ethnic_groupgroup C                                    1.185 0.236695    
## ethnic_groupgroup D                                   -1.167 0.243773    
## ethnic_groupgroup E                                    3.302 0.001025 ** 
## parent_educbachelor's degree                           0.543 0.587093    
## parent_educhigh school                                -0.030 0.975795    
## parent_educmaster's degree                            -2.897 0.003919 ** 
## parent_educsome college                                0.201 0.841106    
## parent_educsome high school                            1.253 0.210932    
## lunch_typestandard                                     2.209 0.027634 *  
## test_prepnone                                          0.732 0.464523    
## parent_marital_statusmarried                          -2.127 0.033844 *  
## parent_marital_statussingle                           -2.993 0.002896 ** 
## parent_marital_statuswidowed                           0.635 0.525561    
## practice_sportregularly                               -0.806 0.420483    
## practice_sportsometimes                               -0.919 0.358598    
## is_first_childyes                                     -0.305 0.760224    
## transport_meansschool_bus                              2.756 0.006061 ** 
## wkly_study_hours> 10                                  -2.070 0.038946 *  
## wkly_study_hours10-May                                -0.648 0.517225    
## writing_score                                          2.342 0.019552 *  
## reading_score                                          2.299 0.021868 *  
## gendermale:writing_score                              -2.613 0.009222 ** 
## ethnic_groupgroup B:test_prepnone                     -0.028 0.977365    
## ethnic_groupgroup C:test_prepnone                     -0.026 0.979606    
## ethnic_groupgroup D:test_prepnone                      1.752 0.080395 .  
## ethnic_groupgroup E:test_prepnone                     -0.123 0.901973    
## ethnic_groupgroup B:is_first_childyes                  0.632 0.527440    
## ethnic_groupgroup C:is_first_childyes                 -1.788 0.074377 .  
## ethnic_groupgroup D:is_first_childyes                 -0.398 0.690452    
## ethnic_groupgroup E:is_first_childyes                 -0.832 0.406060    
## parent_educbachelor's degree:is_first_childyes        -1.732 0.083933 .  
## parent_educhigh school:is_first_childyes               0.691 0.489687    
## parent_educmaster's degree:is_first_childyes           1.491 0.136459    
## parent_educsome college:is_first_childyes             -0.428 0.668933    
## parent_educsome high school:is_first_childyes         -0.476 0.634486    
## lunch_typestandard:is_first_childyes                   2.645 0.008405 ** 
## lunch_typestandard:wkly_study_hours> 10               -2.125 0.034092 *  
## lunch_typestandard:wkly_study_hours10-May             -1.124 0.261502    
## test_prepnone:parent_marital_statusmarried             2.401 0.016706 *  
## test_prepnone:parent_marital_statussingle              2.092 0.036874 *  
## test_prepnone:parent_marital_statuswidowed             0.427 0.669349    
## test_prepnone:transport_meansschool_bus               -2.312 0.021168 *  
## parent_marital_statusmarried:practice_sportregularly   1.787 0.074520 .  
## parent_marital_statussingle:practice_sportregularly    2.902 0.003866 ** 
## parent_marital_statuswidowed:practice_sportregularly  -0.570 0.568833    
## parent_marital_statusmarried:practice_sportsometimes   1.426 0.154547    
## parent_marital_statussingle:practice_sportsometimes    2.071 0.038829 *  
## parent_marital_statuswidowed:practice_sportsometimes  -0.018 0.985548    
## practice_sportregularly:writing_score                  1.853 0.064392 .  
## practice_sportsometimes:writing_score                  2.790 0.005468 ** 
## practice_sportregularly:reading_score                 -1.781 0.075513 .  
## practice_sportsometimes:reading_score                 -2.597 0.009674 ** 
## is_first_childyes:transport_meansschool_bus           -3.799 0.000162 ***
## is_first_childyes:wkly_study_hours> 10                 0.553 0.580328    
## is_first_childyes:wkly_study_hours10-May              -1.780 0.075660 .  
## is_first_childyes:writing_score                        1.735 0.083263 .  
## transport_meansschool_bus:writing_score               -1.641 0.101328    
## wkly_study_hours> 10:reading_score                     3.210 0.001406 ** 
## wkly_study_hours10-May:reading_score                   1.975 0.048840 *  
## writing_score:reading_score                            1.762 0.078609 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.164 on 527 degrees of freedom
## Multiple R-squared:  0.9082, Adjusted R-squared:  0.8974 
## F-statistic: 84.05 on 62 and 527 DF,  p-value: < 2.2e-16

REading Score

df_4_mdl_read2=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,reading_score,writing_score,math_score)
full_fit_read2=lm(reading_score ~ .^2,data=df_4_mdl_read2)
summary(full_fit_read2)
## 
## Call:
## lm(formula = reading_score ~ .^2, data = df_4_mdl_read2)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -8.157 -1.999  0.000  2.306  9.448 
## 
## Coefficients: (6 not defined because of singularities)
##                                                             Estimate Std. Error
## (Intercept)                                               -4.426e+00  1.085e+01
## gendermale                                                 1.402e+00  5.240e+00
## ethnic_groupgroup B                                        7.758e+00  7.293e+00
## ethnic_groupgroup C                                        7.180e+00  6.787e+00
## ethnic_groupgroup D                                        4.785e+00  7.198e+00
## ethnic_groupgroup E                                       -2.946e+00  7.445e+00
## parent_educbachelor's degree                               4.277e+00  7.073e+00
## parent_educhigh school                                    -1.777e+00  5.329e+00
## parent_educmaster's degree                                -3.918e+00  9.371e+00
## parent_educsome college                                    1.329e+00  5.131e+00
## parent_educsome high school                               -3.048e+00  5.280e+00
## lunch_typestandard                                         2.687e+00  4.201e+00
## test_prepnone                                              8.108e-01  4.286e+00
## parent_marital_statusmarried                              -6.063e+00  5.250e+00
## parent_marital_statussingle                               -6.355e+00  6.105e+00
## parent_marital_statuswidowed                              -1.079e+01  1.288e+01
## practice_sportregularly                                   -2.415e+00  6.762e+00
## practice_sportsometimes                                   -3.900e-01  6.671e+00
## is_first_childyes                                          2.294e+00  3.917e+00
## transport_meansschool_bus                                  6.181e+00  3.912e+00
## wkly_study_hours> 10                                       3.133e+00  5.885e+00
## wkly_study_hours10-May                                     6.200e+00  4.543e+00
## writing_score                                              9.889e-01  2.891e-01
## math_score                                                 1.925e-02  2.827e-01
## gendermale:ethnic_groupgroup B                             2.970e-01  3.012e+00
## gendermale:ethnic_groupgroup C                             2.311e+00  2.812e+00
## gendermale:ethnic_groupgroup D                             1.262e+00  2.743e+00
## gendermale:ethnic_groupgroup E                             1.978e+00  3.266e+00
## gendermale:parent_educbachelor's degree                   -2.855e+00  2.374e+00
## gendermale:parent_educhigh school                         -6.166e-01  2.108e+00
## gendermale:parent_educmaster's degree                     -9.504e+00  4.065e+00
## gendermale:parent_educsome college                        -3.343e-01  2.169e+00
## gendermale:parent_educsome high school                     3.952e-02  2.329e+00
## gendermale:lunch_typestandard                             -2.115e+00  1.596e+00
## gendermale:test_prepnone                                  -5.253e-01  1.649e+00
## gendermale:parent_marital_statusmarried                    2.174e+00  2.136e+00
## gendermale:parent_marital_statussingle                    -3.874e-01  2.399e+00
## gendermale:parent_marital_statuswidowed                    1.051e+00  5.789e+00
## gendermale:practice_sportregularly                         3.005e+00  2.716e+00
## gendermale:practice_sportsometimes                         4.005e+00  2.621e+00
## gendermale:is_first_childyes                              -2.639e-01  1.538e+00
## gendermale:transport_meansschool_bus                      -2.728e-01  1.419e+00
## gendermale:wkly_study_hours> 10                           -3.911e+00  2.308e+00
## gendermale:wkly_study_hours10-May                         -1.622e+00  1.716e+00
## gendermale:writing_score                                  -1.191e-01  8.234e-02
## gendermale:math_score                                      9.074e-02  7.834e-02
## ethnic_groupgroup B:parent_educbachelor's degree           1.057e+00  4.470e+00
## ethnic_groupgroup C:parent_educbachelor's degree           2.412e+00  4.449e+00
## ethnic_groupgroup D:parent_educbachelor's degree           2.018e+00  4.420e+00
## ethnic_groupgroup E:parent_educbachelor's degree          -1.433e+00  5.187e+00
## ethnic_groupgroup B:parent_educhigh school                -1.023e+00  2.592e+00
## ethnic_groupgroup C:parent_educhigh school                 7.632e-01  2.452e+00
## ethnic_groupgroup D:parent_educhigh school                -4.872e-01  2.543e+00
## ethnic_groupgroup E:parent_educhigh school                 1.508e+00  2.839e+00
## ethnic_groupgroup B:parent_educmaster's degree             1.676e+01  5.091e+00
## ethnic_groupgroup C:parent_educmaster's degree             1.480e+01  4.727e+00
## ethnic_groupgroup D:parent_educmaster's degree             1.329e+01  4.860e+00
## ethnic_groupgroup E:parent_educmaster's degree             1.189e+01  5.147e+00
## ethnic_groupgroup B:parent_educsome college                5.175e-01  2.898e+00
## ethnic_groupgroup C:parent_educsome college                1.594e+00  2.700e+00
## ethnic_groupgroup D:parent_educsome college                2.192e+00  2.866e+00
## ethnic_groupgroup E:parent_educsome college                6.107e+00  2.860e+00
## ethnic_groupgroup B:parent_educsome high school            3.782e+00  2.779e+00
## ethnic_groupgroup C:parent_educsome high school            3.713e+00  2.558e+00
## ethnic_groupgroup D:parent_educsome high school            2.160e+00  2.604e+00
## ethnic_groupgroup E:parent_educsome high school            7.790e+00  2.829e+00
## ethnic_groupgroup B:lunch_typestandard                     3.824e+00  1.950e+00
## ethnic_groupgroup C:lunch_typestandard                     4.537e+00  1.862e+00
## ethnic_groupgroup D:lunch_typestandard                     6.910e+00  1.871e+00
## ethnic_groupgroup E:lunch_typestandard                     2.204e+00  2.181e+00
## ethnic_groupgroup B:test_prepnone                         -4.163e-01  2.144e+00
## ethnic_groupgroup C:test_prepnone                          1.560e+00  2.017e+00
## ethnic_groupgroup D:test_prepnone                          5.353e-01  2.054e+00
## ethnic_groupgroup E:test_prepnone                          1.851e+00  2.216e+00
## ethnic_groupgroup B:parent_marital_statusmarried           6.731e+00  2.659e+00
## ethnic_groupgroup C:parent_marital_statusmarried           3.053e+00  2.462e+00
## ethnic_groupgroup D:parent_marital_statusmarried           1.614e+00  2.467e+00
## ethnic_groupgroup E:parent_marital_statusmarried           3.724e+00  2.710e+00
## ethnic_groupgroup B:parent_marital_statussingle            8.698e+00  3.046e+00
## ethnic_groupgroup C:parent_marital_statussingle            6.007e+00  2.887e+00
## ethnic_groupgroup D:parent_marital_statussingle            5.892e+00  2.899e+00
## ethnic_groupgroup E:parent_marital_statussingle            1.071e+01  3.238e+00
## ethnic_groupgroup B:parent_marital_statuswidowed          -3.566e+01  3.368e+01
## ethnic_groupgroup C:parent_marital_statuswidowed          -4.413e+01  2.852e+01
## ethnic_groupgroup D:parent_marital_statuswidowed          -1.789e+01  2.687e+01
## ethnic_groupgroup E:parent_marital_statuswidowed                  NA         NA
## ethnic_groupgroup B:practice_sportregularly               -2.261e+00  3.480e+00
## ethnic_groupgroup C:practice_sportregularly               -3.279e+00  3.452e+00
## ethnic_groupgroup D:practice_sportregularly               -2.487e+00  3.761e+00
## ethnic_groupgroup E:practice_sportregularly                1.780e+00  3.590e+00
## ethnic_groupgroup B:practice_sportsometimes               -4.031e-01  3.680e+00
## ethnic_groupgroup C:practice_sportsometimes               -1.435e+00  3.571e+00
## ethnic_groupgroup D:practice_sportsometimes               -1.670e+00  3.875e+00
## ethnic_groupgroup E:practice_sportsometimes                1.511e+00  3.614e+00
## ethnic_groupgroup B:is_first_childyes                     -2.111e+00  1.872e+00
## ethnic_groupgroup C:is_first_childyes                     -2.717e+00  1.742e+00
## ethnic_groupgroup D:is_first_childyes                     -2.832e+00  1.786e+00
## ethnic_groupgroup E:is_first_childyes                     -3.604e+00  2.076e+00
## ethnic_groupgroup B:transport_meansschool_bus             -1.703e+00  1.961e+00
## ethnic_groupgroup C:transport_meansschool_bus             -9.056e-01  1.760e+00
## ethnic_groupgroup D:transport_meansschool_bus              1.526e+00  1.794e+00
## ethnic_groupgroup E:transport_meansschool_bus              7.194e-01  2.179e+00
## ethnic_groupgroup B:wkly_study_hours> 10                  -1.329e+00  3.249e+00
## ethnic_groupgroup C:wkly_study_hours> 10                  -1.667e+00  3.237e+00
## ethnic_groupgroup D:wkly_study_hours> 10                  -4.543e+00  3.271e+00
## ethnic_groupgroup E:wkly_study_hours> 10                  -3.228e+00  3.508e+00
## ethnic_groupgroup B:wkly_study_hours10-May                -6.738e-01  2.640e+00
## ethnic_groupgroup C:wkly_study_hours10-May                -3.220e+00  2.610e+00
## ethnic_groupgroup D:wkly_study_hours10-May                -3.441e+00  2.653e+00
## ethnic_groupgroup E:wkly_study_hours10-May                -5.441e+00  2.887e+00
## ethnic_groupgroup B:writing_score                         -1.839e-01  1.735e-01
## ethnic_groupgroup C:writing_score                         -4.289e-02  1.648e-01
## ethnic_groupgroup D:writing_score                         -8.389e-02  1.631e-01
## ethnic_groupgroup E:writing_score                         -2.687e-02  1.938e-01
## ethnic_groupgroup B:math_score                            -1.872e-02  1.721e-01
## ethnic_groupgroup C:math_score                            -1.279e-01  1.578e-01
## ethnic_groupgroup D:math_score                            -7.158e-02  1.555e-01
## ethnic_groupgroup E:math_score                            -5.867e-02  1.847e-01
## parent_educbachelor's degree:lunch_typestandard           -6.165e-01  1.834e+00
## parent_educhigh school:lunch_typestandard                 -5.979e-01  1.402e+00
## parent_educmaster's degree:lunch_typestandard             -3.498e+00  3.411e+00
## parent_educsome college:lunch_typestandard                -1.325e+00  1.452e+00
## parent_educsome high school:lunch_typestandard            -1.557e-01  1.511e+00
## parent_educbachelor's degree:test_prepnone                -2.759e+00  1.648e+00
## parent_educhigh school:test_prepnone                       5.634e-01  1.520e+00
## parent_educmaster's degree:test_prepnone                   2.793e+00  2.655e+00
## parent_educsome college:test_prepnone                     -1.243e+00  1.465e+00
## parent_educsome high school:test_prepnone                 -7.908e-02  1.433e+00
## parent_educbachelor's degree:parent_marital_statusmarried -1.309e+00  2.883e+00
## parent_educhigh school:parent_marital_statusmarried        1.847e+00  1.966e+00
## parent_educmaster's degree:parent_marital_statusmarried   -6.488e+00  2.832e+00
## parent_educsome college:parent_marital_statusmarried      -1.349e+00  1.863e+00
## parent_educsome high school:parent_marital_statusmarried  -4.263e-01  1.899e+00
## parent_educbachelor's degree:parent_marital_statussingle   9.234e-01  3.226e+00
## parent_educhigh school:parent_marital_statussingle         1.002e+00  2.109e+00
## parent_educmaster's degree:parent_marital_statussingle    -3.543e+00  2.970e+00
## parent_educsome college:parent_marital_statussingle       -8.280e-01  2.027e+00
## parent_educsome high school:parent_marital_statussingle    2.050e+00  2.130e+00
## parent_educbachelor's degree:parent_marital_statuswidowed  3.893e+00  2.711e+01
## parent_educhigh school:parent_marital_statuswidowed        2.680e+01  3.071e+01
## parent_educmaster's degree:parent_marital_statuswidowed    1.524e+01  1.702e+01
## parent_educsome college:parent_marital_statuswidowed       3.226e+01  2.081e+01
## parent_educsome high school:parent_marital_statuswidowed   3.090e+01  2.434e+01
## parent_educbachelor's degree:practice_sportregularly      -4.111e+00  2.830e+00
## parent_educhigh school:practice_sportregularly            -3.260e+00  2.329e+00
## parent_educmaster's degree:practice_sportregularly        -2.114e+00  3.343e+00
## parent_educsome college:practice_sportregularly           -1.400e-01  2.364e+00
## parent_educsome high school:practice_sportregularly       -1.067e+00  2.252e+00
## parent_educbachelor's degree:practice_sportsometimes      -3.320e+00  2.697e+00
## parent_educhigh school:practice_sportsometimes            -1.526e+00  2.238e+00
## parent_educmaster's degree:practice_sportsometimes        -3.695e+00  3.068e+00
## parent_educsome college:practice_sportsometimes           -1.685e+00  2.318e+00
## parent_educsome high school:practice_sportsometimes        1.748e+00  2.120e+00
## parent_educbachelor's degree:is_first_childyes            -1.208e+00  1.617e+00
## parent_educhigh school:is_first_childyes                  -1.886e+00  1.394e+00
## parent_educmaster's degree:is_first_childyes              -4.500e-02  2.641e+00
## parent_educsome college:is_first_childyes                 -1.884e+00  1.367e+00
## parent_educsome high school:is_first_childyes             -2.437e+00  1.382e+00
## parent_educbachelor's degree:transport_meansschool_bus    -7.696e-01  1.662e+00
## parent_educhigh school:transport_meansschool_bus          -8.944e-01  1.320e+00
## parent_educmaster's degree:transport_meansschool_bus      -3.307e+00  2.095e+00
## parent_educsome college:transport_meansschool_bus          1.144e+00  1.326e+00
## parent_educsome high school:transport_meansschool_bus     -1.192e+00  1.412e+00
## parent_educbachelor's degree:wkly_study_hours> 10          2.640e+00  2.425e+00
## parent_educhigh school:wkly_study_hours> 10                1.254e-01  1.987e+00
## parent_educmaster's degree:wkly_study_hours> 10           -3.371e+00  4.819e+00
## parent_educsome college:wkly_study_hours> 10               2.836e+00  2.036e+00
## parent_educsome high school:wkly_study_hours> 10           2.006e+00  2.071e+00
## parent_educbachelor's degree:wkly_study_hours10-May        1.472e+00  1.683e+00
## parent_educhigh school:wkly_study_hours10-May             -2.399e-01  1.564e+00
## parent_educmaster's degree:wkly_study_hours10-May         -6.587e-02  2.515e+00
## parent_educsome college:wkly_study_hours10-May             2.528e+00  1.612e+00
## parent_educsome high school:wkly_study_hours10-May         1.773e-01  1.687e+00
## parent_educbachelor's degree:writing_score                -2.361e-01  1.487e-01
## parent_educhigh school:writing_score                       3.596e-02  1.308e-01
## parent_educmaster's degree:writing_score                  -3.876e-01  2.307e-01
## parent_educsome college:writing_score                     -2.102e-02  1.272e-01
## parent_educsome high school:writing_score                 -2.740e-02  1.325e-01
## parent_educbachelor's degree:math_score                    2.630e-01  1.379e-01
## parent_educhigh school:math_score                          3.693e-02  1.198e-01
## parent_educmaster's degree:math_score                      4.687e-01  2.429e-01
## parent_educsome college:math_score                        -8.838e-03  1.200e-01
## parent_educsome high school:math_score                     5.598e-02  1.257e-01
## lunch_typestandard:test_prepnone                          -1.405e+00  1.127e+00
## lunch_typestandard:parent_marital_statusmarried           -4.861e-01  1.424e+00
## lunch_typestandard:parent_marital_statussingle             1.333e+00  1.657e+00
## lunch_typestandard:parent_marital_statuswidowed            1.830e+01  2.465e+01
## lunch_typestandard:practice_sportregularly                -1.667e+00  1.737e+00
## lunch_typestandard:practice_sportsometimes                -6.638e-01  1.662e+00
## lunch_typestandard:is_first_childyes                      -4.227e-01  1.075e+00
## lunch_typestandard:transport_meansschool_bus              -4.599e-01  1.023e+00
## lunch_typestandard:wkly_study_hours> 10                    9.849e-01  1.564e+00
## lunch_typestandard:wkly_study_hours10-May                 -8.966e-01  1.202e+00
## lunch_typestandard:writing_score                          -1.598e-01  8.786e-02
## lunch_typestandard:math_score                              1.083e-01  8.037e-02
## test_prepnone:parent_marital_statusmarried                 1.929e+00  1.423e+00
## test_prepnone:parent_marital_statussingle                  1.207e+00  1.643e+00
## test_prepnone:parent_marital_statuswidowed                 2.444e+01  1.407e+01
## test_prepnone:practice_sportregularly                      2.596e+00  1.862e+00
## test_prepnone:practice_sportsometimes                      1.233e+00  1.859e+00
## test_prepnone:is_first_childyes                            1.400e+00  1.062e+00
## test_prepnone:transport_meansschool_bus                   -1.152e+00  9.935e-01
## test_prepnone:wkly_study_hours> 10                        -1.361e+00  1.562e+00
## test_prepnone:wkly_study_hours10-May                      -1.755e+00  1.233e+00
## test_prepnone:writing_score                               -6.370e-03  9.285e-02
## test_prepnone:math_score                                   9.062e-03  8.595e-02
## parent_marital_statusmarried:practice_sportregularly      -1.226e+00  2.083e+00
## parent_marital_statussingle:practice_sportregularly       -1.178e+00  2.830e+00
## parent_marital_statuswidowed:practice_sportregularly      -1.507e+01  2.606e+01
## parent_marital_statusmarried:practice_sportsometimes      -1.300e+00  2.046e+00
## parent_marital_statussingle:practice_sportsometimes       -3.030e-01  2.765e+00
## parent_marital_statuswidowed:practice_sportsometimes              NA         NA
## parent_marital_statusmarried:is_first_childyes            -2.096e+00  1.588e+00
## parent_marital_statussingle:is_first_childyes             -1.219e+00  1.728e+00
## parent_marital_statuswidowed:is_first_childyes            -1.659e+01  9.822e+00
## parent_marital_statusmarried:transport_meansschool_bus     5.063e-01  1.284e+00
## parent_marital_statussingle:transport_meansschool_bus     -5.592e-01  1.509e+00
## parent_marital_statuswidowed:transport_meansschool_bus     1.199e+01  6.336e+00
## parent_marital_statusmarried:wkly_study_hours> 10          2.837e+00  2.081e+00
## parent_marital_statussingle:wkly_study_hours> 10           3.864e+00  2.310e+00
## parent_marital_statuswidowed:wkly_study_hours> 10                 NA         NA
## parent_marital_statusmarried:wkly_study_hours10-May       -1.074e+00  1.441e+00
## parent_marital_statussingle:wkly_study_hours10-May        -2.357e+00  1.615e+00
## parent_marital_statuswidowed:wkly_study_hours10-May               NA         NA
## parent_marital_statusmarried:writing_score                 1.329e-01  1.210e-01
## parent_marital_statussingle:writing_score                  1.592e-02  1.356e-01
## parent_marital_statuswidowed:writing_score                        NA         NA
## parent_marital_statusmarried:math_score                   -7.963e-02  1.163e-01
## parent_marital_statussingle:math_score                    -1.076e-02  1.293e-01
## parent_marital_statuswidowed:math_score                           NA         NA
## practice_sportregularly:is_first_childyes                  2.602e+00  1.873e+00
## practice_sportsometimes:is_first_childyes                  1.474e+00  1.820e+00
## practice_sportregularly:transport_meansschool_bus         -1.672e+00  1.591e+00
## practice_sportsometimes:transport_meansschool_bus         -1.272e+00  1.542e+00
## practice_sportregularly:wkly_study_hours> 10              -1.024e+00  2.207e+00
## practice_sportsometimes:wkly_study_hours> 10               4.400e-01  2.182e+00
## practice_sportregularly:wkly_study_hours10-May             1.784e-01  1.692e+00
## practice_sportsometimes:wkly_study_hours10-May             2.696e-02  1.683e+00
## practice_sportregularly:writing_score                      2.752e-01  1.619e-01
## practice_sportsometimes:writing_score                      2.861e-01  1.615e-01
## practice_sportregularly:math_score                        -2.517e-01  1.539e-01
## practice_sportsometimes:math_score                        -3.013e-01  1.503e-01
## is_first_childyes:transport_meansschool_bus                1.054e+00  9.774e-01
## is_first_childyes:wkly_study_hours> 10                    -1.518e+00  1.434e+00
## is_first_childyes:wkly_study_hours10-May                  -8.117e-01  1.089e+00
## is_first_childyes:writing_score                           -3.956e-02  8.887e-02
## is_first_childyes:math_score                               6.301e-02  8.572e-02
## transport_meansschool_bus:wkly_study_hours> 10            -7.879e-01  1.381e+00
## transport_meansschool_bus:wkly_study_hours10-May           8.323e-01  9.872e-01
## transport_meansschool_bus:writing_score                   -5.895e-02  8.555e-02
## transport_meansschool_bus:math_score                      -8.323e-04  7.997e-02
## wkly_study_hours> 10:writing_score                        -2.377e-01  1.372e-01
## wkly_study_hours10-May:writing_score                      -1.762e-01  9.345e-02
## wkly_study_hours> 10:math_score                            2.307e-01  1.285e-01
## wkly_study_hours10-May:math_score                          1.730e-01  9.378e-02
## writing_score:math_score                                   1.096e-03  1.002e-03
##                                                           t value Pr(>|t|)    
## (Intercept)                                                -0.408 0.683671    
## gendermale                                                  0.268 0.789175    
## ethnic_groupgroup B                                         1.064 0.288209    
## ethnic_groupgroup C                                         1.058 0.290906    
## ethnic_groupgroup D                                         0.665 0.506628    
## ethnic_groupgroup E                                        -0.396 0.692529    
## parent_educbachelor's degree                                0.605 0.545774    
## parent_educhigh school                                     -0.333 0.738971    
## parent_educmaster's degree                                 -0.418 0.676188    
## parent_educsome college                                     0.259 0.795820    
## parent_educsome high school                                -0.577 0.564153    
## lunch_typestandard                                          0.640 0.522836    
## test_prepnone                                               0.189 0.850066    
## parent_marital_statusmarried                               -1.155 0.248940    
## parent_marital_statussingle                                -1.041 0.298642    
## parent_marital_statuswidowed                               -0.838 0.402697    
## practice_sportregularly                                    -0.357 0.721210    
## practice_sportsometimes                                    -0.058 0.953423    
## is_first_childyes                                           0.586 0.558477    
## transport_meansschool_bus                                   1.580 0.115044    
## wkly_study_hours> 10                                        0.532 0.594786    
## wkly_study_hours10-May                                      1.365 0.173265    
## writing_score                                               3.421 0.000700 ***
## math_score                                                  0.068 0.945767    
## gendermale:ethnic_groupgroup B                              0.099 0.921492    
## gendermale:ethnic_groupgroup C                              0.822 0.411883    
## gendermale:ethnic_groupgroup D                              0.460 0.645891    
## gendermale:ethnic_groupgroup E                              0.605 0.545254    
## gendermale:parent_educbachelor's degree                    -1.203 0.229964    
## gendermale:parent_educhigh school                          -0.293 0.770029    
## gendermale:parent_educmaster's degree                      -2.338 0.019975 *  
## gendermale:parent_educsome college                         -0.154 0.877599    
## gendermale:parent_educsome high school                      0.017 0.986472    
## gendermale:lunch_typestandard                              -1.325 0.185974    
## gendermale:test_prepnone                                   -0.319 0.750210    
## gendermale:parent_marital_statusmarried                     1.018 0.309505    
## gendermale:parent_marital_statussingle                     -0.161 0.871811    
## gendermale:parent_marital_statuswidowed                     0.182 0.856025    
## gendermale:practice_sportregularly                          1.106 0.269415    
## gendermale:practice_sportsometimes                          1.528 0.127446    
## gendermale:is_first_childyes                               -0.172 0.863917    
## gendermale:transport_meansschool_bus                       -0.192 0.847681    
## gendermale:wkly_study_hours> 10                            -1.695 0.091062 .  
## gendermale:wkly_study_hours10-May                          -0.946 0.345031    
## gendermale:writing_score                                   -1.446 0.149044    
## gendermale:math_score                                       1.158 0.247589    
## ethnic_groupgroup B:parent_educbachelor's degree            0.236 0.813286    
## ethnic_groupgroup C:parent_educbachelor's degree            0.542 0.588126    
## ethnic_groupgroup D:parent_educbachelor's degree            0.457 0.648281    
## ethnic_groupgroup E:parent_educbachelor's degree           -0.276 0.782536    
## ethnic_groupgroup B:parent_educhigh school                 -0.395 0.693296    
## ethnic_groupgroup C:parent_educhigh school                  0.311 0.755742    
## ethnic_groupgroup D:parent_educhigh school                 -0.192 0.848179    
## ethnic_groupgroup E:parent_educhigh school                  0.531 0.595735    
## ethnic_groupgroup B:parent_educmaster's degree              3.291 0.001103 ** 
## ethnic_groupgroup C:parent_educmaster's degree              3.131 0.001896 ** 
## ethnic_groupgroup D:parent_educmaster's degree              2.735 0.006573 ** 
## ethnic_groupgroup E:parent_educmaster's degree              2.310 0.021476 *  
## ethnic_groupgroup B:parent_educsome college                 0.179 0.858399    
## ethnic_groupgroup C:parent_educsome college                 0.590 0.555417    
## ethnic_groupgroup D:parent_educsome college                 0.765 0.444938    
## ethnic_groupgroup E:parent_educsome college                 2.135 0.033479 *  
## ethnic_groupgroup B:parent_educsome high school             1.361 0.174402    
## ethnic_groupgroup C:parent_educsome high school             1.452 0.147562    
## ethnic_groupgroup D:parent_educsome high school             0.829 0.407523    
## ethnic_groupgroup E:parent_educsome high school             2.754 0.006213 ** 
## ethnic_groupgroup B:lunch_typestandard                      1.961 0.050678 .  
## ethnic_groupgroup C:lunch_typestandard                      2.437 0.015326 *  
## ethnic_groupgroup D:lunch_typestandard                      3.694 0.000258 ***
## ethnic_groupgroup E:lunch_typestandard                      1.010 0.313025    
## ethnic_groupgroup B:test_prepnone                          -0.194 0.846211    
## ethnic_groupgroup C:test_prepnone                           0.774 0.439756    
## ethnic_groupgroup D:test_prepnone                           0.261 0.794567    
## ethnic_groupgroup E:test_prepnone                           0.836 0.403997    
## ethnic_groupgroup B:parent_marital_statusmarried            2.532 0.011802 *  
## ethnic_groupgroup C:parent_marital_statusmarried            1.240 0.215834    
## ethnic_groupgroup D:parent_marital_statusmarried            0.654 0.513483    
## ethnic_groupgroup E:parent_marital_statusmarried            1.374 0.170193    
## ethnic_groupgroup B:parent_marital_statussingle             2.856 0.004553 ** 
## ethnic_groupgroup C:parent_marital_statussingle             2.081 0.038193 *  
## ethnic_groupgroup D:parent_marital_statussingle             2.032 0.042887 *  
## ethnic_groupgroup E:parent_marital_statussingle             3.309 0.001038 ** 
## ethnic_groupgroup B:parent_marital_statuswidowed           -1.059 0.290487    
## ethnic_groupgroup C:parent_marital_statuswidowed           -1.547 0.122696    
## ethnic_groupgroup D:parent_marital_statuswidowed           -0.666 0.505847    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                -0.650 0.516300    
## ethnic_groupgroup C:practice_sportregularly                -0.950 0.342711    
## ethnic_groupgroup D:practice_sportregularly                -0.661 0.508816    
## ethnic_groupgroup E:practice_sportregularly                 0.496 0.620400    
## ethnic_groupgroup B:practice_sportsometimes                -0.110 0.912833    
## ethnic_groupgroup C:practice_sportsometimes                -0.402 0.687998    
## ethnic_groupgroup D:practice_sportsometimes                -0.431 0.666704    
## ethnic_groupgroup E:practice_sportsometimes                 0.418 0.676110    
## ethnic_groupgroup B:is_first_childyes                      -1.128 0.260168    
## ethnic_groupgroup C:is_first_childyes                      -1.560 0.119672    
## ethnic_groupgroup D:is_first_childyes                      -1.585 0.113826    
## ethnic_groupgroup E:is_first_childyes                      -1.736 0.083387 .  
## ethnic_groupgroup B:transport_meansschool_bus              -0.869 0.385641    
## ethnic_groupgroup C:transport_meansschool_bus              -0.515 0.607133    
## ethnic_groupgroup D:transport_meansschool_bus               0.850 0.395728    
## ethnic_groupgroup E:transport_meansschool_bus               0.330 0.741479    
## ethnic_groupgroup B:wkly_study_hours> 10                   -0.409 0.682699    
## ethnic_groupgroup C:wkly_study_hours> 10                   -0.515 0.606873    
## ethnic_groupgroup D:wkly_study_hours> 10                   -1.389 0.165797    
## ethnic_groupgroup E:wkly_study_hours> 10                   -0.920 0.358113    
## ethnic_groupgroup B:wkly_study_hours10-May                 -0.255 0.798687    
## ethnic_groupgroup C:wkly_study_hours10-May                 -1.234 0.218172    
## ethnic_groupgroup D:wkly_study_hours10-May                 -1.297 0.195535    
## ethnic_groupgroup E:wkly_study_hours10-May                 -1.885 0.060300 .  
## ethnic_groupgroup B:writing_score                          -1.060 0.289896    
## ethnic_groupgroup C:writing_score                          -0.260 0.794873    
## ethnic_groupgroup D:writing_score                          -0.514 0.607454    
## ethnic_groupgroup E:writing_score                          -0.139 0.889829    
## ethnic_groupgroup B:math_score                             -0.109 0.913438    
## ethnic_groupgroup C:math_score                             -0.810 0.418506    
## ethnic_groupgroup D:math_score                             -0.460 0.645611    
## ethnic_groupgroup E:math_score                             -0.318 0.750960    
## parent_educbachelor's degree:lunch_typestandard            -0.336 0.736915    
## parent_educhigh school:lunch_typestandard                  -0.426 0.670128    
## parent_educmaster's degree:lunch_typestandard              -1.025 0.305876    
## parent_educsome college:lunch_typestandard                 -0.912 0.362201    
## parent_educsome high school:lunch_typestandard             -0.103 0.917960    
## parent_educbachelor's degree:test_prepnone                 -1.674 0.095108 .  
## parent_educhigh school:test_prepnone                        0.371 0.711100    
## parent_educmaster's degree:test_prepnone                    1.052 0.293532    
## parent_educsome college:test_prepnone                      -0.849 0.396664    
## parent_educsome high school:test_prepnone                  -0.055 0.956034    
## parent_educbachelor's degree:parent_marital_statusmarried  -0.454 0.650059    
## parent_educhigh school:parent_marital_statusmarried         0.939 0.348155    
## parent_educmaster's degree:parent_marital_statusmarried    -2.290 0.022604 *  
## parent_educsome college:parent_marital_statusmarried       -0.724 0.469449    
## parent_educsome high school:parent_marital_statusmarried   -0.225 0.822483    
## parent_educbachelor's degree:parent_marital_statussingle    0.286 0.774886    
## parent_educhigh school:parent_marital_statussingle          0.475 0.635097    
## parent_educmaster's degree:parent_marital_statussingle     -1.193 0.233806    
## parent_educsome college:parent_marital_statussingle        -0.408 0.683176    
## parent_educsome high school:parent_marital_statussingle     0.962 0.336653    
## parent_educbachelor's degree:parent_marital_statuswidowed   0.144 0.885883    
## parent_educhigh school:parent_marital_statuswidowed         0.873 0.383467    
## parent_educmaster's degree:parent_marital_statuswidowed     0.896 0.371104    
## parent_educsome college:parent_marital_statuswidowed        1.550 0.122008    
## parent_educsome high school:parent_marital_statuswidowed    1.269 0.205167    
## parent_educbachelor's degree:practice_sportregularly       -1.453 0.147210    
## parent_educhigh school:practice_sportregularly             -1.399 0.162620    
## parent_educmaster's degree:practice_sportregularly         -0.632 0.527626    
## parent_educsome college:practice_sportregularly            -0.059 0.952808    
## parent_educsome high school:practice_sportregularly        -0.474 0.635856    
## parent_educbachelor's degree:practice_sportsometimes       -1.231 0.219177    
## parent_educhigh school:practice_sportsometimes             -0.682 0.495762    
## parent_educmaster's degree:practice_sportsometimes         -1.204 0.229249    
## parent_educsome college:practice_sportsometimes            -0.727 0.467769    
## parent_educsome high school:practice_sportsometimes         0.824 0.410372    
## parent_educbachelor's degree:is_first_childyes             -0.747 0.455633    
## parent_educhigh school:is_first_childyes                   -1.353 0.176995    
## parent_educmaster's degree:is_first_childyes               -0.017 0.986418    
## parent_educsome college:is_first_childyes                  -1.379 0.168938    
## parent_educsome high school:is_first_childyes              -1.763 0.078783 .  
## parent_educbachelor's degree:transport_meansschool_bus     -0.463 0.643567    
## parent_educhigh school:transport_meansschool_bus           -0.677 0.498582    
## parent_educmaster's degree:transport_meansschool_bus       -1.578 0.115479    
## parent_educsome college:transport_meansschool_bus           0.863 0.388977    
## parent_educsome high school:transport_meansschool_bus      -0.844 0.399205    
## parent_educbachelor's degree:wkly_study_hours> 10           1.089 0.277050    
## parent_educhigh school:wkly_study_hours> 10                 0.063 0.949727    
## parent_educmaster's degree:wkly_study_hours> 10            -0.699 0.484758    
## parent_educsome college:wkly_study_hours> 10                1.393 0.164477    
## parent_educsome high school:wkly_study_hours> 10            0.969 0.333468    
## parent_educbachelor's degree:wkly_study_hours10-May         0.875 0.382218    
## parent_educhigh school:wkly_study_hours10-May              -0.153 0.878185    
## parent_educmaster's degree:wkly_study_hours10-May          -0.026 0.979122    
## parent_educsome college:wkly_study_hours10-May              1.569 0.117603    
## parent_educsome high school:wkly_study_hours10-May          0.105 0.916353    
## parent_educbachelor's degree:writing_score                 -1.587 0.113408    
## parent_educhigh school:writing_score                        0.275 0.783591    
## parent_educmaster's degree:writing_score                   -1.680 0.093863 .  
## parent_educsome college:writing_score                      -0.165 0.868787    
## parent_educsome high school:writing_score                  -0.207 0.836274    
## parent_educbachelor's degree:math_score                     1.908 0.057252 .  
## parent_educhigh school:math_score                           0.308 0.758001    
## parent_educmaster's degree:math_score                       1.930 0.054439 .  
## parent_educsome college:math_score                         -0.074 0.941319    
## parent_educsome high school:math_score                      0.445 0.656248    
## lunch_typestandard:test_prepnone                           -1.246 0.213597    
## lunch_typestandard:parent_marital_statusmarried            -0.341 0.733035    
## lunch_typestandard:parent_marital_statussingle              0.804 0.421713    
## lunch_typestandard:parent_marital_statuswidowed             0.743 0.458152    
## lunch_typestandard:practice_sportregularly                 -0.960 0.337845    
## lunch_typestandard:practice_sportsometimes                 -0.400 0.689756    
## lunch_typestandard:is_first_childyes                       -0.393 0.694445    
## lunch_typestandard:transport_meansschool_bus               -0.450 0.653202    
## lunch_typestandard:wkly_study_hours> 10                     0.630 0.529257    
## lunch_typestandard:wkly_study_hours10-May                  -0.746 0.456417    
## lunch_typestandard:writing_score                           -1.819 0.069813 .  
## lunch_typestandard:math_score                               1.348 0.178568    
## test_prepnone:parent_marital_statusmarried                  1.356 0.176095    
## test_prepnone:parent_marital_statussingle                   0.735 0.463029    
## test_prepnone:parent_marital_statuswidowed                  1.737 0.083287 .  
## test_prepnone:practice_sportregularly                       1.395 0.164053    
## test_prepnone:practice_sportsometimes                       0.663 0.507614    
## test_prepnone:is_first_childyes                             1.319 0.188184    
## test_prepnone:transport_meansschool_bus                    -1.160 0.246966    
## test_prepnone:wkly_study_hours> 10                         -0.871 0.384281    
## test_prepnone:wkly_study_hours10-May                       -1.424 0.155352    
## test_prepnone:writing_score                                -0.069 0.945344    
## test_prepnone:math_score                                    0.105 0.916095    
## parent_marital_statusmarried:practice_sportregularly       -0.589 0.556528    
## parent_marital_statussingle:practice_sportregularly        -0.416 0.677513    
## parent_marital_statuswidowed:practice_sportregularly       -0.578 0.563533    
## parent_marital_statusmarried:practice_sportsometimes       -0.635 0.525694    
## parent_marital_statussingle:practice_sportsometimes        -0.110 0.912789    
## parent_marital_statuswidowed:practice_sportsometimes           NA       NA    
## parent_marital_statusmarried:is_first_childyes             -1.320 0.187858    
## parent_marital_statussingle:is_first_childyes              -0.706 0.480761    
## parent_marital_statuswidowed:is_first_childyes             -1.689 0.092194 .  
## parent_marital_statusmarried:transport_meansschool_bus      0.394 0.693668    
## parent_marital_statussingle:transport_meansschool_bus      -0.371 0.711222    
## parent_marital_statuswidowed:transport_meansschool_bus      1.893 0.059273 .  
## parent_marital_statusmarried:wkly_study_hours> 10           1.364 0.173575    
## parent_marital_statussingle:wkly_study_hours> 10            1.673 0.095263 .  
## parent_marital_statuswidowed:wkly_study_hours> 10              NA       NA    
## parent_marital_statusmarried:wkly_study_hours10-May        -0.745 0.456721    
## parent_marital_statussingle:wkly_study_hours10-May         -1.460 0.145295    
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## parent_marital_statusmarried:writing_score                  1.098 0.272979    
## parent_marital_statussingle:writing_score                   0.117 0.906626    
## parent_marital_statuswidowed:writing_score                     NA       NA    
## parent_marital_statusmarried:math_score                    -0.685 0.493846    
## parent_marital_statussingle:math_score                     -0.083 0.933740    
## parent_marital_statuswidowed:math_score                        NA       NA    
## practice_sportregularly:is_first_childyes                   1.389 0.165673    
## practice_sportsometimes:is_first_childyes                   0.810 0.418475    
## practice_sportregularly:transport_meansschool_bus          -1.051 0.294033    
## practice_sportsometimes:transport_meansschool_bus          -0.825 0.409953    
## practice_sportregularly:wkly_study_hours> 10               -0.464 0.642960    
## practice_sportsometimes:wkly_study_hours> 10                0.202 0.840284    
## practice_sportregularly:wkly_study_hours10-May              0.105 0.916088    
## practice_sportsometimes:wkly_study_hours10-May              0.016 0.987230    
## practice_sportregularly:writing_score                       1.700 0.090064 .  
## practice_sportsometimes:writing_score                       1.772 0.077311 .  
## practice_sportregularly:math_score                         -1.635 0.102909    
## practice_sportsometimes:math_score                         -2.005 0.045740 *  
## is_first_childyes:transport_meansschool_bus                 1.078 0.281579    
## is_first_childyes:wkly_study_hours> 10                     -1.059 0.290334    
## is_first_childyes:wkly_study_hours10-May                   -0.746 0.456423    
## is_first_childyes:writing_score                            -0.445 0.656475    
## is_first_childyes:math_score                                0.735 0.462815    
## transport_meansschool_bus:wkly_study_hours> 10             -0.571 0.568631    
## transport_meansschool_bus:wkly_study_hours10-May            0.843 0.399765    
## transport_meansschool_bus:writing_score                    -0.689 0.491249    
## transport_meansschool_bus:math_score                       -0.010 0.991702    
## wkly_study_hours> 10:writing_score                         -1.733 0.084006 .  
## wkly_study_hours10-May:writing_score                       -1.886 0.060213 .  
## wkly_study_hours> 10:math_score                             1.795 0.073500 .  
## wkly_study_hours10-May:math_score                           1.844 0.066012 .  
## writing_score:math_score                                    1.094 0.274947    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.886 on 340 degrees of freedom
## Multiple R-squared:  0.962,  Adjusted R-squared:  0.9342 
## F-statistic: 34.57 on 249 and 340 DF,  p-value: < 2.2e-16
stepwise_model_read2 <- step(full_fit_read2, direction = "both", trace = 1)
## Start:  AIC=1776.62
## reading_score ~ (gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score)^2
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_educ:wkly_study_hours           10     99.04 5234.3 1767.9
## - parent_educ:lunch_type                  5     25.60 5160.8 1769.5
## - ethnic_group:math_score                 4     18.16 5153.4 1770.7
## - parent_marital_status:practice_sport    4     19.43 5154.7 1770.8
## - gender:ethnic_group                     4     19.67 5154.9 1770.9
## - practice_sport:wkly_study_hours         4     25.16 5160.4 1771.5
## - ethnic_group:practice_sport             8     97.36 5232.6 1771.7
## - ethnic_group:writing_score              4     27.67 5162.9 1771.8
## - parent_educ:is_first_child              5     59.40 5194.7 1773.4
## - parent_marital_status:math_score        2     12.48 5147.7 1774.0
## - ethnic_group:test_prep                  4     47.58 5182.8 1774.1
## - parent_marital_status:transport_means   2     14.64 5149.9 1774.3
## - practice_sport:transport_means          2     16.71 5152.0 1774.5
## - ethnic_group:is_first_child             4     52.34 5187.6 1774.6
## - transport_means:math_score              1      0.00 5135.3 1774.6
## - test_prep:writing_score                 1      0.07 5135.3 1774.6
## - test_prep:math_score                    1      0.17 5135.4 1774.6
## - is_first_child:wkly_study_hours         2     17.71 5153.0 1774.7
## - gender:is_first_child                   1      0.44 5135.7 1774.7
## - gender:transport_means                  1      0.56 5135.8 1774.7
## - gender:test_prep                        1      1.53 5136.8 1774.8
## - lunch_type:practice_sport               2     19.36 5154.6 1774.8
## - lunch_type:is_first_child               1      2.33 5137.6 1774.9
## - is_first_child:writing_score            1      2.99 5138.2 1775.0
## - lunch_type:transport_means              1      3.05 5138.3 1775.0
## - transport_means:writing_score           1      7.17 5142.4 1775.4
## - is_first_child:math_score               1      8.16 5143.4 1775.6
## - transport_means:wkly_study_hours        2     29.96 5165.2 1776.0
## - test_prep:parent_marital_status         2     30.23 5165.5 1776.1
## - test_prep:wkly_study_hours              2     30.65 5165.9 1776.1
## - parent_marital_status:is_first_child    2     30.66 5165.9 1776.1
## - parent_marital_status:writing_score     2     31.63 5166.9 1776.2
## - lunch_type:wkly_study_hours             2     31.64 5166.9 1776.2
## <none>                                                5135.2 1776.6
## - is_first_child:transport_means          1     17.57 5152.8 1776.6
## - writing_score:math_score                1     18.06 5153.3 1776.7
## - gender:practice_sport                   2     36.55 5171.8 1776.8
## - lunch_type:parent_marital_status        2     37.01 5172.3 1776.9
## - gender:math_score                       1     20.26 5155.5 1776.9
## - test_prep:transport_means               1     20.31 5155.6 1777.0
## - practice_sport:is_first_child           2     39.42 5174.7 1777.1
## - lunch_type:test_prep                    1     23.45 5158.7 1777.3
## - parent_educ:writing_score               5     94.58 5229.8 1777.4
## - parent_educ:transport_means             5     94.90 5230.1 1777.4
## - gender:wkly_study_hours                 2     43.49 5178.7 1777.6
## - test_prep:is_first_child                1     26.26 5161.5 1777.6
## - gender:lunch_type                       1     26.53 5161.8 1777.7
## - gender:parent_marital_status            2     44.65 5179.9 1777.7
## - lunch_type:math_score                   1     27.44 5162.7 1777.8
## - test_prep:practice_sport                2     45.43 5180.7 1777.8
## - parent_educ:test_prep                   5     98.73 5234.0 1777.8
## - gender:writing_score                    1     31.59 5166.8 1778.2
## - practice_sport:writing_score            2     49.70 5185.0 1778.3
## - gender:parent_educ                      5    105.13 5240.4 1778.6
## - practice_sport:math_score               2     60.80 5196.1 1779.6
## - wkly_study_hours:math_score             2     65.25 5200.5 1780.1
## - wkly_study_hours:writing_score          2     67.41 5202.7 1780.3
## - lunch_type:writing_score                1     49.97 5185.2 1780.3
## - parent_educ:math_score                  5    121.69 5256.9 1780.4
## - ethnic_group:transport_means            4    109.59 5244.8 1781.1
## - parent_educ:parent_marital_status      11    235.69 5370.9 1781.1
## - ethnic_group:wkly_study_hours           8    199.07 5334.3 1783.1
## - parent_educ:practice_sport             10    235.54 5370.8 1783.1
## - parent_marital_status:wkly_study_hours  4    154.17 5289.4 1786.1
## - ethnic_group:parent_educ               20    524.88 5660.1 1794.0
## - ethnic_group:lunch_type                 4    244.78 5380.0 1796.1
## - ethnic_group:parent_marital_status      8    321.58 5456.8 1796.5
## 
## Step:  AIC=1767.89
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:ethnic_group + gender:parent_educ + gender:lunch_type + 
##     gender:test_prep + gender:parent_marital_status + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + ethnic_group:math_score + parent_educ:lunch_type + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:math_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_educ:lunch_type                  5     32.14 5266.4 1761.5
## - ethnic_group:math_score                 4     18.61 5252.9 1762.0
## - ethnic_group:writing_score              4     21.90 5256.2 1762.3
## - parent_marital_status:practice_sport    4     23.11 5257.4 1762.5
## - gender:ethnic_group                     4     24.33 5258.6 1762.6
## - practice_sport:wkly_study_hours         4     37.01 5271.3 1764.0
## - ethnic_group:practice_sport             8    113.81 5348.1 1764.6
## - ethnic_group:is_first_child             4     42.08 5276.4 1764.6
## - parent_marital_status:math_score        2     13.13 5247.4 1765.4
## - is_first_child:wkly_study_hours         2     14.26 5248.5 1765.5
## - parent_marital_status:transport_means   2     14.69 5249.0 1765.5
## - practice_sport:transport_means          2     16.02 5250.3 1765.7
## - lunch_type:practice_sport               2     16.65 5250.9 1765.8
## - parent_educ:is_first_child              5     70.86 5305.2 1765.8
## - gender:is_first_child                   1      0.03 5234.3 1765.9
## - test_prep:math_score                    1      0.04 5234.3 1765.9
## - test_prep:writing_score                 1      0.13 5234.4 1765.9
## - transport_means:math_score              1      0.59 5234.9 1766.0
## - gender:test_prep                        1      0.99 5235.3 1766.0
## - lunch_type:is_first_child               1      1.11 5235.4 1766.0
## - gender:transport_means                  1      2.02 5236.3 1766.1
## - lunch_type:transport_means              1      3.77 5238.1 1766.3
## - is_first_child:writing_score            1      4.08 5238.4 1766.3
## - ethnic_group:test_prep                  4     60.96 5295.2 1766.7
## - is_first_child:math_score               1      9.38 5243.7 1767.0
## - parent_marital_status:writing_score     2     31.56 5265.8 1767.4
## - parent_educ:writing_score               5     85.74 5320.0 1767.5
## - writing_score:math_score                1     14.35 5248.6 1767.5
## - is_first_child:transport_means          1     14.50 5248.8 1767.5
## - parent_marital_status:is_first_child    2     32.50 5266.8 1767.5
## - transport_means:writing_score           1     14.93 5249.2 1767.6
## - test_prep:wkly_study_hours              2     33.96 5268.2 1767.7
## - lunch_type:test_prep                    1     16.60 5250.9 1767.8
## - test_prep:is_first_child                1     16.92 5251.2 1767.8
## - parent_educ:transport_means             5     89.08 5323.4 1767.8
## - test_prep:parent_marital_status         2     35.26 5269.6 1767.8
## <none>                                                5234.3 1767.9
## - transport_means:wkly_study_hours        2     35.66 5270.0 1767.9
## - lunch_type:parent_marital_status        2     36.82 5271.1 1768.0
## - practice_sport:is_first_child           2     39.13 5273.4 1768.3
## - gender:math_score                       1     23.03 5257.3 1768.5
## - lunch_type:math_score                   1     24.34 5258.6 1768.6
## - gender:parent_marital_status            2     42.49 5276.8 1768.7
## - gender:lunch_type                       1     24.76 5259.0 1768.7
## - test_prep:practice_sport                2     43.27 5277.6 1768.8
## - test_prep:transport_means               1     26.63 5260.9 1768.9
## - gender:parent_educ                      5    103.22 5337.5 1769.4
## - gender:writing_score                    1     33.17 5267.5 1769.6
## - gender:practice_sport                   2     53.46 5287.8 1769.9
## - parent_educ:math_score                  5    108.90 5343.2 1770.0
## - gender:wkly_study_hours                 2     58.51 5292.8 1770.5
## - practice_sport:writing_score            2     60.14 5294.4 1770.6
## - ethnic_group:transport_means            4     97.19 5331.5 1770.7
## - lunch_type:writing_score                1     43.30 5277.6 1770.8
## - lunch_type:wkly_study_hours             2     62.65 5296.9 1770.9
## - ethnic_group:wkly_study_hours           8    177.77 5412.1 1771.6
## - wkly_study_hours:math_score             2     72.48 5306.8 1772.0
## - parent_educ:parent_marital_status      11    238.98 5473.3 1772.2
## - wkly_study_hours:writing_score          2     77.99 5312.3 1772.6
## - practice_sport:math_score               2     80.83 5315.1 1772.9
## - parent_educ:practice_sport             10    231.64 5465.9 1773.4
## - parent_educ:test_prep                   5    142.86 5377.2 1773.8
## + parent_educ:wkly_study_hours           10     99.04 5135.2 1776.6
## - parent_marital_status:wkly_study_hours  4    160.99 5395.3 1777.8
## - ethnic_group:parent_educ               20    533.53 5767.8 1785.2
## - ethnic_group:lunch_type                 4    231.80 5466.1 1785.5
## - ethnic_group:parent_marital_status      8    310.43 5544.7 1785.9
## 
## Step:  AIC=1761.5
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:ethnic_group + gender:parent_educ + gender:lunch_type + 
##     gender:test_prep + gender:parent_marital_status + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + ethnic_group:math_score + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:writing_score + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:math_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:math_score                 4     23.66 5290.1 1756.2
## - gender:ethnic_group                     4     25.16 5291.6 1756.3
## - ethnic_group:writing_score              4     25.95 5292.4 1756.4
## - parent_marital_status:practice_sport    4     25.97 5292.4 1756.4
## - practice_sport:wkly_study_hours         4     31.79 5298.2 1757.0
## - ethnic_group:is_first_child             4     39.67 5306.1 1757.9
## - parent_marital_status:math_score        2      8.91 5275.3 1758.5
## - parent_marital_status:transport_means   2     10.76 5277.2 1758.7
## - ethnic_group:practice_sport             8    120.14 5386.6 1758.8
## - is_first_child:wkly_study_hours         2     13.18 5279.6 1759.0
## - practice_sport:transport_means          2     15.73 5282.2 1759.3
## - parent_educ:is_first_child              5     71.51 5337.9 1759.5
## - gender:is_first_child                   1      0.00 5266.4 1759.5
## - test_prep:writing_score                 1      0.04 5266.5 1759.5
## - transport_means:math_score              1      0.29 5266.7 1759.5
## - test_prep:math_score                    1      0.33 5266.8 1759.5
## - lunch_type:is_first_child               1      1.81 5268.2 1759.7
## - lunch_type:transport_means              1      2.05 5268.5 1759.7
## - gender:test_prep                        1      2.06 5268.5 1759.7
## - gender:transport_means                  1      2.09 5268.5 1759.7
## - lunch_type:practice_sport               2     21.40 5287.8 1759.9
## - is_first_child:writing_score            1      3.62 5270.1 1759.9
## - parent_educ:writing_score               5     78.62 5345.0 1760.2
## - parent_marital_status:writing_score     2     25.19 5291.6 1760.3
## - is_first_child:math_score               1      8.25 5274.7 1760.4
## - ethnic_group:test_prep                  4     66.19 5332.6 1760.9
## - transport_means:writing_score           1     13.11 5279.5 1761.0
## - parent_educ:transport_means             5     85.44 5351.9 1761.0
## - is_first_child:transport_means          1     14.02 5280.4 1761.1
## - writing_score:math_score                1     15.93 5282.4 1761.3
## <none>                                                5266.4 1761.5
## - test_prep:is_first_child                1     18.16 5284.6 1761.5
## - parent_marital_status:is_first_child    2     36.16 5302.6 1761.5
## - test_prep:parent_marital_status         2     36.26 5302.7 1761.5
## - transport_means:wkly_study_hours        2     36.28 5302.7 1761.5
## - gender:parent_marital_status            2     36.95 5303.4 1761.6
## - gender:lunch_type                       1     21.22 5287.6 1761.9
## - gender:math_score                       1     22.00 5288.4 1762.0
## - lunch_type:test_prep                    1     22.17 5288.6 1762.0
## - lunch_type:math_score                   1     22.77 5289.2 1762.0
## - test_prep:wkly_study_hours              2     41.04 5307.5 1762.1
## - gender:parent_educ                      5     96.27 5362.7 1762.2
## - lunch_type:parent_marital_status        2     43.24 5309.7 1762.3
## - practice_sport:is_first_child           2     45.52 5312.0 1762.6
## - test_prep:transport_means               1     28.32 5294.8 1762.7
## - test_prep:practice_sport                2     47.65 5314.1 1762.8
## - gender:writing_score                    1     32.09 5298.5 1763.1
## - gender:practice_sport                   2     53.88 5320.3 1763.5
## - parent_educ:math_score                  5    109.55 5376.0 1763.7
## - parent_educ:parent_marital_status      11    225.10 5491.5 1764.2
## - ethnic_group:transport_means            4     96.39 5362.8 1764.2
## - practice_sport:writing_score            2     61.03 5327.5 1764.3
## - lunch_type:writing_score                1     43.24 5309.7 1764.3
## - lunch_type:wkly_study_hours             2     61.88 5328.3 1764.4
## - ethnic_group:wkly_study_hours           8    174.21 5440.6 1764.7
## - gender:wkly_study_hours                 2     70.77 5337.2 1765.4
## - wkly_study_hours:math_score             2     80.04 5346.5 1766.4
## - practice_sport:math_score               2     83.53 5350.0 1766.8
## - wkly_study_hours:writing_score          2     88.59 5355.0 1767.3
## + parent_educ:lunch_type                  5     32.14 5234.3 1767.9
## - parent_educ:test_prep                   5    151.06 5417.5 1768.2
## - parent_educ:practice_sport             10    250.79 5517.2 1769.0
## + parent_educ:wkly_study_hours           10    105.59 5160.8 1769.5
## - parent_marital_status:wkly_study_hours  4    172.74 5439.2 1772.5
## - ethnic_group:lunch_type                 4    231.69 5498.1 1778.9
## - ethnic_group:parent_educ               20    539.60 5806.0 1779.0
## - ethnic_group:parent_marital_status      8    318.72 5585.2 1780.2
## 
## Step:  AIC=1756.15
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:ethnic_group + gender:parent_educ + gender:lunch_type + 
##     gender:test_prep + gender:parent_marital_status + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:math_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:ethnic_group                     4      7.59 5297.7 1749.0
## - parent_marital_status:practice_sport    4     26.65 5316.7 1751.1
## - practice_sport:wkly_study_hours         4     32.72 5322.8 1751.8
## - parent_marital_status:transport_means   2      6.89 5297.0 1752.9
## - ethnic_group:is_first_child             4     45.10 5335.2 1753.2
## - parent_marital_status:math_score        2     10.01 5300.1 1753.3
## - ethnic_group:practice_sport             8    119.75 5409.8 1753.3
## - parent_educ:writing_score               5     68.85 5358.9 1753.8
## - is_first_child:wkly_study_hours         2     14.98 5305.1 1753.8
## - practice_sport:transport_means          2     17.75 5307.8 1754.1
## - gender:is_first_child                   1      0.01 5290.1 1754.2
## - test_prep:writing_score                 1      0.02 5290.1 1754.2
## - test_prep:math_score                    1      0.27 5290.4 1754.2
## - transport_means:math_score              1      1.09 5291.2 1754.3
## - ethnic_group:test_prep                  4     55.38 5345.5 1754.3
## - parent_educ:is_first_child              5     74.08 5364.2 1754.3
## - gender:test_prep                        1      1.99 5292.1 1754.4
## - lunch_type:is_first_child               1      2.31 5292.4 1754.4
## - is_first_child:writing_score            1      3.13 5293.2 1754.5
## - gender:transport_means                  1      3.16 5293.3 1754.5
## - lunch_type:transport_means              1      3.51 5293.6 1754.5
## - is_first_child:math_score               1      7.55 5297.6 1755.0
## - lunch_type:practice_sport               2     26.13 5316.2 1755.0
## - parent_marital_status:writing_score     2     26.48 5316.6 1755.1
## - parent_educ:transport_means             5     84.43 5374.5 1755.5
## - gender:parent_educ                      5     85.80 5375.9 1755.6
## - is_first_child:transport_means          1     14.87 5305.0 1755.8
## - writing_score:math_score                1     14.99 5305.1 1755.8
## - transport_means:writing_score           1     17.05 5307.1 1756.0
## <none>                                                5290.1 1756.2
## - transport_means:wkly_study_hours        2     37.02 5327.1 1756.3
## - gender:parent_marital_status            2     38.31 5328.4 1756.4
## - test_prep:parent_marital_status         2     38.33 5328.4 1756.4
## - parent_marital_status:is_first_child    2     38.74 5328.8 1756.5
## - lunch_type:test_prep                    1     20.81 5310.9 1756.5
## - test_prep:is_first_child                1     21.44 5311.5 1756.5
## - test_prep:wkly_study_hours              2     39.48 5329.6 1756.5
## - gender:lunch_type                       1     22.23 5312.3 1756.6
## - lunch_type:math_score                   1     23.83 5313.9 1756.8
## - gender:math_score                       1     25.68 5315.8 1757.0
## - lunch_type:parent_marital_status        2     45.57 5335.7 1757.2
## - test_prep:transport_means               1     28.43 5318.5 1757.3
## - parent_educ:math_score                  5    102.76 5392.8 1757.5
## - test_prep:practice_sport                2     48.96 5339.1 1757.6
## - practice_sport:is_first_child           2     49.49 5339.6 1757.6
## - gender:writing_score                    1     36.83 5326.9 1758.2
## - ethnic_group:transport_means            4     93.01 5383.1 1758.4
## - parent_educ:parent_marital_status      11    223.99 5514.1 1758.6
## - gender:practice_sport                   2     60.84 5350.9 1758.9
## - lunch_type:writing_score                1     44.10 5334.2 1759.0
## - lunch_type:wkly_study_hours             2     64.25 5354.3 1759.3
## - practice_sport:writing_score            2     65.61 5355.7 1759.4
## - ethnic_group:wkly_study_hours           8    181.55 5471.6 1760.0
## - gender:wkly_study_hours                 2     82.95 5373.0 1761.3
## + ethnic_group:math_score                 4     23.66 5266.4 1761.5
## - parent_educ:test_prep                   5    142.97 5433.1 1761.9
## + parent_educ:lunch_type                  5     37.20 5252.9 1762.0
## - ethnic_group:writing_score              4    126.62 5416.7 1762.1
## - practice_sport:math_score               2     92.30 5382.4 1762.3
## - wkly_study_hours:math_score             2     92.57 5382.7 1762.4
## - parent_educ:practice_sport             10    249.75 5539.8 1763.4
## - wkly_study_hours:writing_score          2    101.96 5392.0 1763.4
## + parent_educ:wkly_study_hours           10    104.81 5185.3 1764.3
## - parent_marital_status:wkly_study_hours  4    178.15 5468.2 1767.7
## - ethnic_group:lunch_type                 4    229.86 5519.9 1773.2
## - ethnic_group:parent_educ               20    551.40 5841.5 1774.6
## - ethnic_group:parent_marital_status      8    336.50 5626.6 1776.5
## 
## Step:  AIC=1748.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:practice_sport + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + parent_marital_status:math_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_marital_status:practice_sport    4     25.00 5322.7 1743.8
## - practice_sport:wkly_study_hours         4     31.86 5329.5 1744.5
## - parent_marital_status:transport_means   2      7.88 5305.6 1745.9
## - ethnic_group:is_first_child             4     44.07 5341.8 1745.9
## - parent_marital_status:math_score        2      9.50 5307.2 1746.0
## - parent_educ:writing_score               5     67.83 5365.5 1746.5
## - ethnic_group:test_prep                  4     50.49 5348.2 1746.6
## - ethnic_group:practice_sport             8    124.29 5422.0 1746.7
## - is_first_child:wkly_study_hours         2     16.79 5314.5 1746.9
## - gender:is_first_child                   1      0.00 5297.7 1747.0
## - test_prep:writing_score                 1      0.02 5297.7 1747.0
## - test_prep:math_score                    1      0.15 5297.8 1747.0
## - practice_sport:transport_means          2     18.16 5315.8 1747.0
## - parent_educ:is_first_child              5     73.08 5370.8 1747.1
## - transport_means:math_score              1      1.18 5298.9 1747.1
## - gender:test_prep                        1      1.40 5299.1 1747.2
## - lunch_type:is_first_child               1      2.55 5300.2 1747.3
## - is_first_child:writing_score            1      2.84 5300.5 1747.3
## - gender:transport_means                  1      3.22 5300.9 1747.3
## - lunch_type:transport_means              1      3.69 5301.4 1747.4
## - parent_marital_status:writing_score     2     25.65 5323.3 1747.8
## - is_first_child:math_score               1      7.64 5305.3 1747.8
## - lunch_type:practice_sport               2     25.84 5323.5 1747.9
## - gender:parent_educ                      5     86.68 5384.4 1748.6
## - is_first_child:transport_means          1     14.45 5312.1 1748.6
## - parent_educ:transport_means             5     87.85 5385.5 1748.7
## - test_prep:parent_marital_status         2     35.32 5333.0 1748.9
## - transport_means:writing_score           1     17.63 5315.3 1749.0
## - transport_means:wkly_study_hours        2     35.89 5333.6 1749.0
## <none>                                                5297.7 1749.0
## - gender:parent_marital_status            2     36.76 5334.4 1749.1
## - writing_score:math_score                1     18.76 5316.4 1749.1
## - lunch_type:test_prep                    1     20.27 5318.0 1749.2
## - parent_marital_status:is_first_child    2     38.83 5336.5 1749.3
## - test_prep:is_first_child                1     21.36 5319.0 1749.4
## - test_prep:wkly_study_hours              2     40.98 5338.7 1749.5
## - lunch_type:math_score                   1     24.20 5321.9 1749.7
## - gender:lunch_type                       1     25.11 5322.8 1749.8
## - lunch_type:parent_marital_status        2     46.56 5344.2 1750.2
## - test_prep:transport_means               1     28.63 5326.3 1750.2
## - parent_educ:math_score                  5    102.65 5400.3 1750.3
## - practice_sport:is_first_child           2     49.62 5347.3 1750.5
## - test_prep:practice_sport                2     51.00 5348.7 1750.6
## - gender:math_score                       1     33.79 5331.5 1750.7
## - ethnic_group:transport_means            4     95.01 5392.7 1751.5
## - gender:writing_score                    1     41.50 5339.2 1751.6
## - parent_educ:parent_marital_status      11    228.15 5525.8 1751.9
## - lunch_type:wkly_study_hours             2     63.39 5361.1 1752.0
## - gender:practice_sport                   2     64.06 5361.7 1752.1
## - lunch_type:writing_score                1     46.23 5343.9 1752.1
## - practice_sport:writing_score            2     69.95 5367.6 1752.7
## - ethnic_group:wkly_study_hours           8    181.07 5478.8 1752.8
## - gender:wkly_study_hours                 2     82.47 5380.2 1754.1
## - parent_educ:test_prep                   5    139.88 5437.6 1754.4
## + parent_educ:lunch_type                  5     36.07 5261.6 1755.0
## - wkly_study_hours:math_score             2     90.93 5388.6 1755.0
## - practice_sport:math_score               2     98.83 5396.5 1755.9
## - wkly_study_hours:writing_score          2    100.68 5398.4 1756.1
## + gender:ethnic_group                     4      7.59 5290.1 1756.2
## + ethnic_group:math_score                 4      6.09 5291.6 1756.3
## - parent_educ:practice_sport             10    252.44 5550.1 1756.5
## + parent_educ:wkly_study_hours           10    103.62 5194.1 1757.3
## - ethnic_group:writing_score              4    176.73 5474.4 1760.3
## - parent_marital_status:wkly_study_hours  4    180.09 5477.8 1760.7
## - ethnic_group:lunch_type                 4    235.12 5532.8 1766.6
## - ethnic_group:parent_marital_status      8    332.53 5630.2 1768.9
## - ethnic_group:parent_educ               20    574.25 5871.9 1769.7
## 
## Step:  AIC=1743.77
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     parent_marital_status:math_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:writing_score + 
##     transport_means:math_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - practice_sport:wkly_study_hours         4     35.95 5358.6 1739.7
## - ethnic_group:is_first_child             4     43.27 5366.0 1740.5
## - parent_marital_status:math_score        2      8.31 5331.0 1740.7
## - parent_marital_status:transport_means   2      9.38 5332.1 1740.8
## - parent_educ:writing_score               5     64.98 5387.7 1740.9
## - parent_educ:is_first_child              5     70.69 5393.4 1741.5
## - practice_sport:transport_means          2     17.40 5340.1 1741.7
## - ethnic_group:test_prep                  4     54.26 5376.9 1741.8
## - test_prep:math_score                    1      0.06 5322.7 1741.8
## - gender:is_first_child                   1      0.13 5322.8 1741.8
## - test_prep:writing_score                 1      0.13 5322.8 1741.8
## - transport_means:math_score              1      0.87 5323.6 1741.9
## - lunch_type:is_first_child               1      0.90 5323.6 1741.9
## - is_first_child:wkly_study_hours         2     19.24 5341.9 1741.9
## - gender:test_prep                        1      1.54 5324.2 1741.9
## - lunch_type:transport_means              1      2.56 5325.2 1742.0
## - gender:transport_means                  1      3.34 5326.0 1742.1
## - is_first_child:writing_score            1      4.19 5326.9 1742.2
## - parent_marital_status:writing_score     2     23.09 5345.8 1742.3
## - lunch_type:practice_sport               2     26.96 5349.7 1742.8
## - is_first_child:transport_means          1     10.09 5332.8 1742.9
## - is_first_child:math_score               1     10.22 5332.9 1742.9
## - parent_educ:transport_means             5     83.88 5406.6 1743.0
## - gender:parent_educ                      5     85.35 5408.0 1743.2
## - ethnic_group:practice_sport             8    145.31 5468.0 1743.7
## - transport_means:wkly_study_hours        2     35.36 5358.0 1743.7
## - transport_means:writing_score           1     18.06 5340.7 1743.8
## <none>                                                5322.7 1743.8
## - gender:parent_marital_status            2     37.16 5359.9 1743.9
## - test_prep:is_first_child                1     19.22 5341.9 1743.9
## - test_prep:parent_marital_status         2     37.89 5360.6 1744.0
## - parent_educ:parent_marital_status      12    224.32 5547.0 1744.1
## - lunch_type:test_prep                    1     21.68 5344.4 1744.2
## - parent_marital_status:is_first_child    2     40.22 5362.9 1744.2
## - writing_score:math_score                1     22.15 5344.8 1744.2
## - test_prep:wkly_study_hours              2     46.29 5369.0 1744.9
## - lunch_type:math_score                   1     28.65 5351.3 1744.9
## - parent_educ:math_score                  5    101.82 5424.5 1745.0
## - gender:lunch_type                       1     29.83 5352.5 1745.1
## - lunch_type:parent_marital_status        2     49.87 5372.6 1745.3
## - test_prep:transport_means               1     31.76 5354.4 1745.3
## - test_prep:practice_sport                2     51.57 5374.3 1745.5
## - gender:math_score                       1     36.34 5359.0 1745.8
## - practice_sport:is_first_child           2     54.59 5377.3 1745.8
## - lunch_type:wkly_study_hours             2     56.88 5379.6 1746.0
## - ethnic_group:transport_means            4     95.44 5418.1 1746.3
## - gender:practice_sport                   2     62.49 5385.2 1746.7
## - gender:writing_score                    1     44.93 5367.6 1746.7
## - ethnic_group:wkly_study_hours           8    178.86 5501.6 1747.3
## - practice_sport:writing_score            2     68.21 5390.9 1747.3
## - lunch_type:writing_score                1     56.03 5378.7 1748.0
## - parent_educ:test_prep                   5    136.96 5459.6 1748.8
## - gender:wkly_study_hours                 2     83.19 5405.9 1748.9
## + parent_marital_status:practice_sport    4     25.00 5297.7 1749.0
## + parent_educ:lunch_type                  5     39.74 5282.9 1749.3
## - wkly_study_hours:math_score             2     88.07 5410.8 1749.5
## - practice_sport:math_score               2     98.15 5420.8 1750.5
## - wkly_study_hours:writing_score          2     99.05 5421.7 1750.7
## + ethnic_group:math_score                 4      8.09 5314.6 1750.9
## + gender:ethnic_group                     4      5.95 5316.7 1751.1
## + parent_educ:wkly_study_hours           10    104.49 5218.2 1752.1
## - parent_educ:practice_sport             10    268.47 5591.2 1752.8
## - ethnic_group:writing_score              4    173.82 5496.5 1754.7
## - parent_marital_status:wkly_study_hours  4    184.74 5507.4 1755.9
## - ethnic_group:lunch_type                 4    241.75 5564.4 1762.0
## - ethnic_group:parent_marital_status      8    336.31 5659.0 1763.9
## - ethnic_group:parent_educ               20    580.45 5903.1 1764.8
## 
## Step:  AIC=1739.74
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     parent_marital_status:math_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_marital_status:math_score        2      6.75 5365.4 1736.5
## - parent_marital_status:transport_means   2      6.92 5365.6 1736.5
## - ethnic_group:is_first_child             4     49.47 5408.1 1737.2
## - parent_educ:writing_score               5     67.87 5426.5 1737.2
## - gender:is_first_child                   1      0.07 5358.7 1737.8
## - test_prep:writing_score                 1      0.10 5358.7 1737.8
## - test_prep:math_score                    1      0.14 5358.8 1737.8
## - transport_means:math_score              1      0.30 5358.9 1737.8
## - practice_sport:transport_means          2     18.99 5377.6 1737.8
## - is_first_child:wkly_study_hours         2     19.12 5377.8 1737.8
## - lunch_type:is_first_child               1      1.09 5359.7 1737.9
## - lunch_type:transport_means              1      1.34 5360.0 1737.9
## - ethnic_group:test_prep                  4     56.21 5414.9 1737.9
## - is_first_child:writing_score            1      1.63 5360.3 1737.9
## - gender:test_prep                        1      1.85 5360.5 1738.0
## - parent_marital_status:writing_score     2     20.34 5379.0 1738.0
## - gender:transport_means                  1      2.26 5360.9 1738.0
## - lunch_type:practice_sport               2     23.96 5382.6 1738.4
## - is_first_child:math_score               1      6.35 5365.0 1738.4
## - parent_educ:is_first_child              5     80.26 5438.9 1738.5
## - parent_educ:transport_means             5     81.56 5440.2 1738.7
## - is_first_child:transport_means          1     10.60 5369.2 1738.9
## - transport_means:wkly_study_hours        2     31.07 5389.7 1739.2
## - parent_educ:parent_marital_status      12    217.16 5575.8 1739.2
## - gender:parent_marital_status            2     33.34 5392.0 1739.4
## - ethnic_group:practice_sport             8    144.67 5503.3 1739.5
## - transport_means:writing_score           1     16.33 5375.0 1739.5
## - gender:parent_educ                      5     89.77 5448.4 1739.5
## - lunch_type:test_prep                    1     17.71 5376.3 1739.7
## <none>                                                5358.6 1739.7
## - test_prep:parent_marital_status         2     36.93 5395.6 1739.8
## - writing_score:math_score                1     19.75 5378.4 1739.9
## - parent_marital_status:is_first_child    2     38.61 5397.2 1740.0
## - test_prep:is_first_child                1     21.29 5379.9 1740.1
## - test_prep:transport_means               1     24.99 5383.6 1740.5
## - lunch_type:parent_marital_status        2     43.46 5402.1 1740.5
## - lunch_type:math_score                   1     29.57 5388.2 1741.0
## - parent_educ:math_score                  5    105.92 5464.6 1741.3
## - gender:lunch_type                       1     32.59 5391.2 1741.3
## - test_prep:practice_sport                2     51.04 5409.7 1741.3
## - practice_sport:is_first_child           2     51.99 5410.6 1741.4
## - lunch_type:wkly_study_hours             2     52.73 5411.4 1741.5
## - test_prep:wkly_study_hours              2     53.60 5412.2 1741.6
## - ethnic_group:transport_means            4     93.78 5452.4 1742.0
## - ethnic_group:wkly_study_hours           8    171.19 5529.8 1742.3
## - gender:math_score                       1     42.05 5400.7 1742.3
## - gender:practice_sport                   2     61.33 5420.0 1742.5
## - gender:writing_score                    1     48.64 5407.3 1743.1
## - practice_sport:writing_score            2     67.16 5425.8 1743.1
## + practice_sport:wkly_study_hours         4     35.95 5322.7 1743.8
## - lunch_type:writing_score                1     57.04 5415.7 1744.0
## + parent_marital_status:practice_sport    4     29.09 5329.5 1744.5
## - parent_educ:test_prep                   5    144.63 5503.3 1745.5
## - gender:wkly_study_hours                 2     89.60 5448.2 1745.5
## + parent_educ:lunch_type                  5     34.29 5324.3 1746.0
## - practice_sport:math_score               2     95.36 5454.0 1746.2
## - wkly_study_hours:math_score             2     95.95 5454.6 1746.2
## + ethnic_group:math_score                 4      8.87 5349.8 1746.8
## + gender:ethnic_group                     4      5.31 5353.3 1747.2
## + parent_educ:wkly_study_hours           10    111.66 5247.0 1747.3
## - wkly_study_hours:writing_score          2    109.57 5468.2 1747.7
## - parent_educ:practice_sport             10    260.25 5618.9 1747.7
## - parent_marital_status:wkly_study_hours  4    187.40 5546.0 1752.0
## - ethnic_group:writing_score              4    200.58 5559.2 1753.4
## - ethnic_group:lunch_type                 4    241.00 5599.6 1757.7
## - ethnic_group:parent_educ               20    562.34 5921.0 1758.6
## - ethnic_group:parent_marital_status      8    333.71 5692.3 1759.4
## 
## Step:  AIC=1736.48
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     is_first_child:writing_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:writing_score + 
##     transport_means:math_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_marital_status:transport_means   2      7.82 5373.2 1733.3
## - ethnic_group:is_first_child             4     46.78 5412.2 1733.6
## - parent_educ:writing_score               5     65.75 5431.1 1733.7
## - parent_educ:parent_marital_status      13    218.65 5584.0 1734.0
## - test_prep:math_score                    1      0.05 5365.4 1734.5
## - gender:is_first_child                   1      0.17 5365.6 1734.5
## - transport_means:math_score              1      0.20 5365.6 1734.5
## - test_prep:writing_score                 1      0.22 5365.6 1734.5
## - ethnic_group:test_prep                  4     55.82 5421.2 1734.6
## - is_first_child:writing_score            1      1.38 5366.8 1734.6
## - lunch_type:transport_means              1      1.43 5366.8 1734.6
## - gender:test_prep                        1      1.66 5367.0 1734.7
## - lunch_type:is_first_child               1      1.70 5367.1 1734.7
## - is_first_child:wkly_study_hours         2     19.95 5385.3 1734.7
## - practice_sport:transport_means          2     19.99 5385.4 1734.7
## - gender:transport_means                  1      2.10 5367.5 1734.7
## - parent_educ:is_first_child              5     78.51 5443.9 1735.0
## - lunch_type:practice_sport               2     23.57 5389.0 1735.1
## - is_first_child:math_score               1      6.09 5371.5 1735.2
## - parent_educ:transport_means             5     81.96 5447.3 1735.4
## - parent_marital_status:writing_score     2     27.29 5392.7 1735.5
## - is_first_child:transport_means          1     11.04 5376.4 1735.7
## - ethnic_group:practice_sport             8    141.76 5507.1 1735.9
## - transport_means:wkly_study_hours        2     32.99 5398.4 1736.1
## - test_prep:parent_marital_status         2     33.08 5398.5 1736.1
## - transport_means:writing_score           1     15.38 5380.8 1736.2
## - lunch_type:test_prep                    1     16.06 5381.4 1736.2
## <none>                                                5365.4 1736.5
## - parent_marital_status:is_first_child    2     37.06 5402.4 1736.5
## - writing_score:math_score                1     19.43 5384.8 1736.6
## - gender:parent_educ                      5     93.47 5458.9 1736.7
## - gender:parent_marital_status            2     39.19 5404.6 1736.8
## - test_prep:is_first_child                1     22.38 5387.8 1736.9
## - test_prep:transport_means               1     25.63 5391.0 1737.3
## - lunch_type:math_score                   1     27.25 5392.6 1737.5
## - parent_educ:math_score                  5    102.69 5468.1 1737.7
## - gender:lunch_type                       1     30.19 5395.6 1737.8
## - test_prep:practice_sport                2     50.07 5415.5 1738.0
## - practice_sport:is_first_child           2     51.54 5416.9 1738.1
## - lunch_type:wkly_study_hours             2     53.76 5419.1 1738.4
## - lunch_type:parent_marital_status        2     54.19 5419.6 1738.4
## - test_prep:wkly_study_hours              2     54.98 5420.4 1738.5
## - ethnic_group:transport_means            4     96.35 5461.7 1739.0
## - ethnic_group:wkly_study_hours           8    172.80 5538.2 1739.2
## - gender:math_score                       1     44.06 5409.4 1739.3
## - gender:practice_sport                   2     63.97 5429.4 1739.5
## + parent_marital_status:math_score        2      6.75 5358.6 1739.7
## - gender:writing_score                    1     50.39 5415.8 1740.0
## - practice_sport:writing_score            2     69.85 5435.2 1740.1
## - lunch_type:writing_score                1     53.02 5418.4 1740.3
## + practice_sport:wkly_study_hours         4     34.38 5331.0 1740.7
## + parent_marital_status:practice_sport    4     27.79 5337.6 1741.4
## - parent_educ:test_prep                   5    145.01 5510.4 1742.2
## - gender:wkly_study_hours                 2     93.92 5459.3 1742.7
## + parent_educ:lunch_type                  5     31.22 5334.2 1743.0
## - wkly_study_hours:math_score             2     99.25 5464.6 1743.3
## + ethnic_group:math_score                 4     10.74 5354.6 1743.3
## - practice_sport:math_score               2    101.15 5466.5 1743.5
## + gender:ethnic_group                     4      5.35 5360.0 1743.9
## + parent_educ:wkly_study_hours           10    110.59 5254.8 1744.2
## - wkly_study_hours:writing_score          2    112.00 5477.4 1744.7
## - parent_educ:practice_sport             10    267.55 5632.9 1745.2
## - parent_marital_status:wkly_study_hours  4    187.07 5552.4 1748.7
## - ethnic_group:writing_score              4    203.33 5568.7 1750.4
## - ethnic_group:lunch_type                 4    241.21 5606.6 1754.4
## - ethnic_group:parent_educ               20    560.46 5925.8 1755.1
## - ethnic_group:parent_marital_status      9    352.61 5718.0 1756.0
## 
## Step:  AIC=1733.34
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:writing_score + 
##     parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_educ:writing_score               5     62.21 5435.4 1730.1
## - ethnic_group:is_first_child             4     49.66 5422.9 1730.8
## - is_first_child:wkly_study_hours         2     17.50 5390.7 1731.3
## - test_prep:math_score                    1      0.04 5373.2 1731.3
## - test_prep:writing_score                 1      0.24 5373.4 1731.4
## - transport_means:math_score              1      0.30 5373.5 1731.4
## - gender:is_first_child                   1      0.40 5373.6 1731.4
## - is_first_child:writing_score            1      0.75 5374.0 1731.4
## - lunch_type:transport_means              1      1.60 5374.8 1731.5
## - gender:test_prep                        1      1.65 5374.9 1731.5
## - lunch_type:is_first_child               1      1.89 5375.1 1731.5
## - gender:transport_means                  1      1.95 5375.2 1731.6
## - ethnic_group:test_prep                  4     57.94 5431.1 1731.7
## - is_first_child:math_score               1      4.83 5378.0 1731.9
## - practice_sport:transport_means          2     23.36 5396.6 1731.9
## - lunch_type:practice_sport               2     23.58 5396.8 1731.9
## - parent_educ:is_first_child              5     79.63 5452.8 1732.0
## - ethnic_group:practice_sport             8    138.61 5511.8 1732.4
## - gender:parent_marital_status            3     47.12 5420.3 1732.5
## - is_first_child:transport_means          1     10.85 5384.1 1732.5
## - parent_educ:transport_means             5     87.76 5461.0 1732.9
## - lunch_type:test_prep                    1     15.02 5388.2 1733.0
## - transport_means:writing_score           1     15.13 5388.3 1733.0
## - transport_means:wkly_study_hours        2     33.71 5406.9 1733.0
## - test_prep:parent_marital_status         2     34.63 5407.8 1733.1
## - gender:parent_educ                      5     90.19 5463.4 1733.2
## - parent_educ:parent_marital_status      14    259.65 5632.9 1733.2
## <none>                                                5373.2 1733.3
## - parent_marital_status:is_first_child    2     36.89 5410.1 1733.4
## - writing_score:math_score                1     21.54 5394.7 1733.7
## - test_prep:transport_means               1     22.24 5395.5 1733.8
## - test_prep:is_first_child                1     22.84 5396.0 1733.8
## - parent_educ:math_score                  5     97.72 5470.9 1734.0
## - lunch_type:math_score                   1     24.71 5397.9 1734.0
## - gender:lunch_type                       1     28.29 5401.5 1734.4
## - practice_sport:is_first_child           2     48.85 5422.1 1734.7
## - test_prep:practice_sport                2     51.77 5425.0 1735.0
## - ethnic_group:transport_means            4     90.53 5463.7 1735.2
## - lunch_type:wkly_study_hours             2     55.67 5428.9 1735.4
## - test_prep:wkly_study_hours              2     58.01 5431.2 1735.7
## - gender:practice_sport                   2     60.67 5433.9 1736.0
## - gender:math_score                       1     43.56 5416.8 1736.1
## - ethnic_group:wkly_study_hours           8    175.34 5548.5 1736.3
## + parent_marital_status:transport_means   2      7.82 5365.4 1736.5
## + parent_marital_status:math_score        2      7.65 5365.6 1736.5
## - parent_marital_status:writing_score     3     85.53 5458.7 1736.7
## - practice_sport:writing_score            2     68.12 5441.3 1736.8
## - lunch_type:writing_score                1     50.08 5423.3 1736.8
## - gender:writing_score                    1     51.32 5424.5 1737.0
## - lunch_type:parent_marital_status        3     96.14 5469.3 1737.8
## + practice_sport:wkly_study_hours         4     31.75 5341.5 1737.8
## + parent_marital_status:practice_sport    4     28.76 5344.4 1738.2
## - parent_educ:test_prep                   5    142.60 5515.8 1738.8
## - gender:wkly_study_hours                 2     96.52 5469.7 1739.8
## - practice_sport:math_score               2     97.50 5470.7 1740.0
## + ethnic_group:math_score                 4     10.01 5363.2 1740.2
## + parent_educ:lunch_type                  5     26.59 5346.6 1740.4
## + gender:ethnic_group                     4      6.35 5366.9 1740.7
## - wkly_study_hours:math_score             2    105.20 5478.4 1740.8
## + parent_educ:wkly_study_hours           10    108.59 5264.6 1741.3
## - parent_educ:practice_sport             10    265.61 5638.8 1741.8
## - wkly_study_hours:writing_score          2    119.85 5493.1 1742.4
## - parent_marital_status:wkly_study_hours  5    184.32 5557.5 1743.2
## - ethnic_group:writing_score              4    220.03 5593.2 1749.0
## - ethnic_group:lunch_type                 4    242.89 5616.1 1751.4
## - ethnic_group:parent_marital_status     10    362.53 5735.7 1751.9
## - ethnic_group:parent_educ               20    560.54 5933.7 1751.9
## 
## Step:  AIC=1730.14
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:is_first_child             4     49.50 5484.9 1727.5
## - is_first_child:wkly_study_hours         2     14.94 5450.4 1727.8
## - ethnic_group:test_prep                  4     52.13 5487.5 1727.8
## - parent_educ:transport_means             5     74.03 5509.4 1728.1
## - test_prep:math_score                    1      0.11 5435.5 1728.2
## - is_first_child:writing_score            1      0.40 5435.8 1728.2
## - transport_means:math_score              1      0.47 5435.9 1728.2
## - gender:test_prep                        1      0.55 5436.0 1728.2
## - lunch_type:transport_means              1      0.60 5436.0 1728.2
## - lunch_type:is_first_child               1      0.62 5436.0 1728.2
## - gender:is_first_child                   1      0.65 5436.1 1728.2
## - test_prep:writing_score                 1      1.37 5436.8 1728.3
## - gender:transport_means                  1      2.45 5437.9 1728.4
## - practice_sport:transport_means          2     22.14 5457.6 1728.5
## - is_first_child:math_score               1      4.16 5439.6 1728.6
## - transport_means:wkly_study_hours        2     25.62 5461.0 1728.9
## - lunch_type:practice_sport               2     25.99 5461.4 1729.0
## - parent_educ:parent_marital_status      14    256.02 5691.4 1729.3
## - gender:parent_marital_status            3     49.04 5484.4 1729.4
## - is_first_child:transport_means          1     12.12 5447.5 1729.5
## - lunch_type:test_prep                    1     13.70 5449.1 1729.6
## - ethnic_group:practice_sport             8    145.66 5581.1 1729.7
## - transport_means:writing_score           1     16.37 5451.8 1729.9
## - gender:parent_educ                      5     91.96 5527.4 1730.0
## <none>                                                5435.4 1730.1
## - test_prep:parent_marital_status         2     37.42 5472.8 1730.2
## - parent_educ:is_first_child              5     93.82 5529.2 1730.2
## - writing_score:math_score                1     19.83 5455.2 1730.3
## - test_prep:transport_means               1     21.10 5456.5 1730.4
## - lunch_type:math_score                   1     21.62 5457.0 1730.5
## - gender:lunch_type                       1     24.34 5459.8 1730.8
## - test_prep:practice_sport                2     45.03 5480.4 1731.0
## - test_prep:is_first_child                1     28.04 5463.5 1731.2
## - parent_marital_status:is_first_child    2     47.13 5482.5 1731.2
## - ethnic_group:wkly_study_hours           8    165.80 5601.2 1731.9
## - test_prep:wkly_study_hours              2     54.71 5490.1 1732.0
## - parent_educ:math_score                  5    110.99 5546.4 1732.1
## - lunch_type:wkly_study_hours             2     55.35 5490.8 1732.1
## - ethnic_group:transport_means            4     96.71 5532.1 1732.5
## - lunch_type:writing_score                1     40.87 5476.3 1732.6
## - practice_sport:is_first_child           2     61.19 5496.6 1732.7
## - gender:practice_sport                   2     63.54 5499.0 1733.0
## - practice_sport:writing_score            2     64.88 5500.3 1733.1
## + parent_educ:writing_score               5     62.21 5373.2 1733.3
## + parent_marital_status:math_score        2      5.37 5430.0 1733.5
## + parent_marital_status:transport_means   2      4.28 5431.1 1733.7
## - gender:math_score                       1     54.88 5490.3 1734.1
## - parent_marital_status:writing_score     3     93.13 5528.5 1734.2
## + practice_sport:wkly_study_hours         4     35.09 5400.3 1734.3
## - gender:writing_score                    1     62.81 5498.2 1734.9
## - lunch_type:parent_marital_status        3    102.72 5538.1 1735.2
## - gender:wkly_study_hours                 2     84.05 5519.5 1735.2
## + parent_marital_status:practice_sport    4     26.59 5408.8 1735.2
## - wkly_study_hours:math_score             2     92.27 5527.7 1736.1
## - practice_sport:math_score               2     95.97 5531.4 1736.5
## + ethnic_group:math_score                 4      9.81 5425.6 1737.1
## - parent_educ:test_prep                   5    160.90 5596.3 1737.3
## - wkly_study_hours:writing_score          2    105.68 5541.1 1737.5
## + gender:ethnic_group                     4      5.12 5430.3 1737.6
## - parent_educ:practice_sport             10    260.47 5695.9 1737.8
## + parent_educ:lunch_type                  5     20.57 5414.8 1737.9
## + parent_educ:wkly_study_hours           10    107.36 5328.1 1738.4
## - parent_marital_status:wkly_study_hours  5    194.94 5630.4 1740.9
## - ethnic_group:writing_score              4    224.64 5660.1 1746.0
## - ethnic_group:lunch_type                 4    234.65 5670.1 1747.1
## - ethnic_group:parent_educ               20    552.81 5988.2 1747.3
## - ethnic_group:parent_marital_status     10    363.05 5798.5 1748.3
## 
## Step:  AIC=1727.48
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - is_first_child:wkly_study_hours         2      8.98 5493.9 1724.5
## - parent_educ:transport_means             5     67.47 5552.4 1724.7
## - ethnic_group:test_prep                  4     49.82 5534.7 1724.8
## - test_prep:math_score                    1      0.00 5484.9 1725.5
## - lunch_type:transport_means              1      0.01 5484.9 1725.5
## - is_first_child:writing_score            1      0.01 5484.9 1725.5
## - transport_means:math_score              1      0.03 5484.9 1725.5
## - gender:test_prep                        1      0.54 5485.5 1725.5
## - lunch_type:is_first_child               1      0.72 5485.6 1725.6
## - is_first_child:math_score               1      0.76 5485.7 1725.6
## - test_prep:writing_score                 1      0.84 5485.8 1725.6
## - gender:transport_means                  1      1.08 5486.0 1725.6
## - practice_sport:transport_means          2     19.77 5504.7 1725.6
## - gender:is_first_child                   1      2.62 5487.5 1725.8
## - transport_means:wkly_study_hours        2     23.06 5508.0 1726.0
## - parent_educ:parent_marital_status      14    254.99 5739.9 1726.3
## - gender:parent_marital_status            3     45.65 5530.6 1726.4
## - parent_educ:is_first_child              5     84.71 5569.6 1726.5
## - lunch_type:practice_sport               2     29.23 5514.1 1726.6
## - ethnic_group:practice_sport             8    143.06 5628.0 1726.7
## - transport_means:writing_score           1     13.35 5498.3 1726.9
## - lunch_type:test_prep                    1     17.40 5502.3 1727.3
## <none>                                                5484.9 1727.5
## - lunch_type:math_score                   1     19.17 5504.1 1727.5
## - test_prep:transport_means               1     21.54 5506.5 1727.8
## - gender:parent_educ                      5     97.30 5582.2 1727.9
## - gender:lunch_type                       1     22.29 5507.2 1727.9
## - writing_score:math_score                1     22.36 5507.3 1727.9
## - is_first_child:transport_means          1     22.89 5507.8 1727.9
## - parent_marital_status:is_first_child    2     41.76 5526.7 1728.0
## - test_prep:parent_marital_status         2     45.56 5530.5 1728.4
## - test_prep:practice_sport                2     45.66 5530.6 1728.4
## - test_prep:wkly_study_hours              2     46.50 5531.4 1728.5
## - ethnic_group:wkly_study_hours           8    161.99 5646.9 1728.7
## - test_prep:is_first_child                1     35.28 5520.2 1729.3
## - lunch_type:wkly_study_hours             2     54.73 5539.6 1729.3
## - lunch_type:writing_score                1     37.42 5522.3 1729.5
## - practice_sport:writing_score            2     61.59 5546.5 1730.1
## + ethnic_group:is_first_child             4     49.50 5435.4 1730.1
## - gender:practice_sport                   2     62.26 5547.2 1730.1
## - practice_sport:is_first_child           2     64.05 5549.0 1730.3
## - gender:math_score                       1     49.04 5534.0 1730.7
## + parent_educ:writing_score               5     62.05 5422.9 1730.8
## + parent_marital_status:transport_means   2      6.29 5478.6 1730.8
## - ethnic_group:transport_means            4    108.02 5592.9 1731.0
## + practice_sport:wkly_study_hours         4     40.60 5444.3 1731.1
## + parent_marital_status:math_score        2      3.37 5481.5 1731.1
## - parent_educ:math_score                  5    128.64 5613.6 1731.2
## - parent_marital_status:writing_score     3     91.67 5576.6 1731.3
## - gender:writing_score                    1     56.93 5541.8 1731.6
## - gender:wkly_study_hours                 2     78.89 5563.8 1731.9
## - lunch_type:parent_marital_status        3     97.87 5582.8 1731.9
## - wkly_study_hours:math_score             2     83.40 5568.3 1732.4
## + parent_marital_status:practice_sport    4     28.17 5456.7 1732.5
## - practice_sport:math_score               2     95.91 5580.8 1733.7
## - parent_educ:test_prep                   5    153.21 5638.1 1733.7
## - wkly_study_hours:writing_score          2     99.08 5584.0 1734.0
## + ethnic_group:math_score                 4      6.41 5478.5 1734.8
## + gender:ethnic_group                     4      3.54 5481.4 1735.1
## + parent_educ:lunch_type                  5     19.41 5465.5 1735.4
## - parent_educ:practice_sport             10    267.31 5752.2 1735.6
## + parent_educ:wkly_study_hours           10     96.02 5388.9 1737.1
## - parent_marital_status:wkly_study_hours  5    199.26 5684.2 1738.5
## - ethnic_group:parent_educ               20    541.67 6026.6 1743.0
## - ethnic_group:writing_score              4    230.81 5715.7 1743.8
## - ethnic_group:lunch_type                 4    254.22 5739.1 1746.2
## - ethnic_group:parent_marital_status     10    409.97 5894.9 1750.0
## 
## Step:  AIC=1724.45
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:writing_score + 
##     transport_means:math_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - ethnic_group:test_prep                  4     50.95 5544.8 1721.9
## - parent_educ:transport_means             5     72.69 5566.6 1722.2
## - transport_means:math_score              1      0.00 5493.9 1722.5
## - test_prep:math_score                    1      0.02 5493.9 1722.5
## - lunch_type:transport_means              1      0.05 5493.9 1722.5
## - is_first_child:writing_score            1      0.06 5494.0 1722.5
## - is_first_child:math_score               1      0.30 5494.2 1722.5
## - practice_sport:transport_means          2     19.09 5513.0 1722.5
## - lunch_type:is_first_child               1      0.51 5494.4 1722.5
## - test_prep:writing_score                 1      0.62 5494.5 1722.5
## - gender:test_prep                        1      0.87 5494.8 1722.5
## - gender:transport_means                  1      0.89 5494.8 1722.5
## - gender:is_first_child                   1      3.17 5497.1 1722.8
## - parent_educ:parent_marital_status      14    252.13 5746.0 1722.9
## - transport_means:wkly_study_hours        2     24.78 5518.7 1723.1
## - gender:parent_marital_status            3     45.63 5539.5 1723.3
## - parent_educ:is_first_child              5     83.65 5577.5 1723.4
## - ethnic_group:practice_sport             8    142.97 5636.9 1723.6
## - transport_means:writing_score           1     12.78 5506.7 1723.8
## - lunch_type:practice_sport               2     32.32 5526.2 1723.9
## - lunch_type:test_prep                    1     16.40 5510.3 1724.2
## <none>                                                5493.9 1724.5
## - gender:parent_educ                      5     93.95 5587.8 1724.5
## - lunch_type:math_score                   1     18.94 5512.8 1724.5
## - test_prep:transport_means               1     20.03 5513.9 1724.6
## - writing_score:math_score                1     21.34 5515.2 1724.7
## - gender:lunch_type                       1     21.47 5515.4 1724.8
## - is_first_child:transport_means          1     23.56 5517.5 1725.0
## - test_prep:wkly_study_hours              2     42.48 5536.4 1725.0
## - parent_marital_status:is_first_child    2     42.64 5536.5 1725.0
## - test_prep:practice_sport                2     45.04 5538.9 1725.3
## - ethnic_group:wkly_study_hours           8    159.38 5653.3 1725.3
## - test_prep:parent_marital_status         2     46.18 5540.1 1725.4
## - lunch_type:writing_score                1     36.88 5530.8 1726.4
## - practice_sport:writing_score            2     56.79 5550.7 1726.5
## - lunch_type:wkly_study_hours             2     57.21 5551.1 1726.6
## - test_prep:is_first_child                1     39.32 5533.2 1726.7
## - gender:practice_sport                   2     58.90 5552.8 1726.7
## - practice_sport:is_first_child           2     65.62 5559.5 1727.5
## + is_first_child:wkly_study_hours         2      8.98 5484.9 1727.5
## - gender:math_score                       1     48.73 5542.6 1727.7
## + ethnic_group:is_first_child             4     43.55 5450.4 1727.8
## - ethnic_group:transport_means            4    107.39 5601.3 1727.9
## + parent_marital_status:transport_means   2      4.43 5489.5 1728.0
## + practice_sport:wkly_study_hours         4     41.43 5452.5 1728.0
## + parent_educ:writing_score               5     59.63 5434.3 1728.0
## + parent_marital_status:math_score        2      3.49 5490.4 1728.1
## - parent_marital_status:writing_score     3     91.40 5585.3 1728.2
## - gender:writing_score                    1     56.13 5550.0 1728.5
## - gender:wkly_study_hours                 2     75.86 5569.8 1728.5
## - lunch_type:parent_marital_status        3     96.95 5590.9 1728.8
## - parent_educ:math_score                  5    135.88 5629.8 1728.9
## - wkly_study_hours:math_score             2     81.42 5575.3 1729.1
## + parent_marital_status:practice_sport    4     30.77 5463.1 1729.1
## - practice_sport:math_score               2     91.09 5585.0 1730.2
## - parent_educ:test_prep                   5    151.58 5645.5 1730.5
## - wkly_study_hours:writing_score          2     97.71 5591.6 1730.8
## + ethnic_group:math_score                 4      5.97 5487.9 1731.8
## + gender:ethnic_group                     4      4.13 5489.8 1732.0
## + parent_educ:lunch_type                  5     20.98 5472.9 1732.2
## - parent_educ:practice_sport             10    268.69 5762.6 1732.6
## + parent_educ:wkly_study_hours           10     96.11 5397.8 1734.0
## - parent_marital_status:wkly_study_hours  5    203.04 5696.9 1735.9
## - ethnic_group:parent_educ               20    540.16 6034.1 1739.8
## - ethnic_group:writing_score              4    235.62 5729.5 1741.2
## - ethnic_group:lunch_type                 4    252.93 5746.8 1743.0
## - ethnic_group:parent_marital_status     10    413.83 5907.7 1747.3
## 
## Step:  AIC=1721.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:writing_score + 
##     transport_means:math_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_educ:transport_means             5     73.94 5618.8 1719.7
## - practice_sport:transport_means          2     18.67 5563.5 1719.9
## - lunch_type:transport_means              1      0.00 5544.8 1719.9
## - gender:transport_means                  1      0.02 5544.9 1719.9
## - test_prep:writing_score                 1      0.09 5544.9 1719.9
## - is_first_child:math_score               1      0.11 5545.0 1719.9
## - transport_means:wkly_study_hours        2     19.11 5564.0 1719.9
## - is_first_child:writing_score            1      0.29 5545.1 1719.9
## - transport_means:math_score              1      0.48 5545.3 1720.0
## - lunch_type:is_first_child               1      1.05 5545.9 1720.0
## - test_prep:math_score                    1      1.13 5546.0 1720.0
## - gender:test_prep                        1      1.61 5546.5 1720.1
## - gender:is_first_child                   1      3.96 5548.8 1720.3
## - ethnic_group:practice_sport             8    137.21 5682.0 1720.3
## - transport_means:writing_score           1      8.26 5553.1 1720.8
## - gender:parent_marital_status            3     47.35 5592.2 1720.9
## - parent_educ:is_first_child              5     86.75 5631.6 1721.1
## - lunch_type:math_score                   1     14.22 5559.1 1721.4
## - gender:parent_educ                      5     90.41 5635.3 1721.4
## - parent_educ:parent_marital_status      14    265.70 5810.5 1721.5
## - lunch_type:practice_sport               2     34.53 5579.4 1721.6
## - gender:lunch_type                       1     16.29 5561.1 1721.6
## - lunch_type:test_prep                    1     18.11 5563.0 1721.8
## <none>                                                5544.8 1721.9
## - test_prep:wkly_study_hours              2     38.73 5583.6 1722.0
## - test_prep:transport_means               1     22.21 5567.1 1722.2
## - writing_score:math_score                1     23.54 5568.4 1722.4
## - test_prep:practice_sport                2     43.67 5588.5 1722.5
## - parent_marital_status:is_first_child    2     44.25 5589.1 1722.6
## - is_first_child:transport_means          1     25.71 5570.6 1722.6
## - test_prep:parent_marital_status         2     47.89 5592.7 1723.0
## - practice_sport:writing_score            2     49.93 5594.8 1723.2
## - gender:practice_sport                   2     51.64 5596.5 1723.4
## - lunch_type:writing_score                1     33.99 5578.8 1723.5
## - practice_sport:is_first_child           2     53.57 5598.4 1723.6
## - lunch_type:wkly_study_hours             2     58.06 5602.9 1724.0
## - test_prep:is_first_child                1     40.92 5585.8 1724.2
## + ethnic_group:test_prep                  4     50.95 5493.9 1724.5
## + is_first_child:wkly_study_hours         2     10.11 5534.7 1724.8
## - gender:math_score                       1     47.04 5591.9 1724.9
## - parent_educ:math_score                  5    125.85 5670.7 1725.1
## + parent_marital_status:transport_means   2      6.66 5538.2 1725.2
## - gender:wkly_study_hours                 2     70.75 5615.6 1725.4
## + practice_sport:wkly_study_hours         4     41.94 5502.9 1725.4
## - ethnic_group:transport_means            4    109.52 5654.4 1725.4
## - gender:writing_score                    1     53.05 5597.9 1725.5
## + parent_marital_status:math_score        2      3.50 5541.3 1725.5
## + ethnic_group:is_first_child             4     40.43 5504.4 1725.6
## - ethnic_group:wkly_study_hours           8    191.07 5735.9 1725.9
## - wkly_study_hours:math_score             2     77.76 5622.6 1726.1
## + parent_educ:writing_score               5     53.48 5491.4 1726.2
## - parent_marital_status:writing_score     3     97.54 5642.4 1726.2
## + parent_marital_status:practice_sport    4     34.33 5510.5 1726.2
## - practice_sport:math_score               2     79.54 5624.4 1726.3
## - lunch_type:parent_marital_status        3    100.88 5645.7 1726.5
## - parent_educ:test_prep                   5    139.67 5684.5 1726.6
## - wkly_study_hours:writing_score          2     91.86 5636.7 1727.6
## - parent_educ:practice_sport             10    264.05 5808.9 1729.3
## + ethnic_group:math_score                 4      3.80 5541.0 1729.5
## + parent_educ:lunch_type                  5     22.03 5522.8 1729.5
## + gender:ethnic_group                     4      2.81 5542.0 1729.6
## + parent_educ:wkly_study_hours           10    109.21 5435.6 1730.2
## - parent_marital_status:wkly_study_hours  5    207.68 5752.5 1733.6
## - ethnic_group:parent_educ               20    568.34 6113.2 1739.5
## - ethnic_group:writing_score              4    258.59 5803.4 1740.8
## - ethnic_group:lunch_type                 4    261.59 5806.4 1741.1
## - ethnic_group:parent_marital_status     10    402.96 5947.8 1743.3
## 
## Step:  AIC=1719.71
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:writing_score + 
##     transport_means:math_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - practice_sport:transport_means          2     12.44 5631.2 1717.0
## - gender:transport_means                  1      0.08 5618.9 1717.7
## - is_first_child:writing_score            1      0.15 5618.9 1717.7
## - test_prep:writing_score                 1      0.25 5619.0 1717.7
## - transport_means:math_score              1      0.30 5619.1 1717.7
## - lunch_type:transport_means              1      0.42 5619.2 1717.8
## - test_prep:math_score                    1      0.65 5619.4 1717.8
## - lunch_type:is_first_child               1      0.83 5619.6 1717.8
## - transport_means:wkly_study_hours        2     19.99 5638.8 1717.8
## - gender:test_prep                        1      0.98 5619.8 1717.8
## - is_first_child:math_score               1      1.48 5620.3 1717.9
## - gender:is_first_child                   1      1.48 5620.3 1717.9
## - parent_educ:is_first_child              5     80.44 5699.2 1718.1
## - gender:parent_educ                      5     82.21 5701.0 1718.3
## - gender:parent_marital_status            3     44.63 5663.4 1718.4
## - parent_educ:parent_marital_status      14    260.26 5879.0 1718.4
## - ethnic_group:practice_sport             8    143.17 5762.0 1718.6
## - transport_means:writing_score           1      8.99 5627.8 1718.7
## - gender:lunch_type                       1     10.12 5628.9 1718.8
## - lunch_type:math_score                   1     11.04 5629.8 1718.9
## - lunch_type:test_prep                    1     14.11 5632.9 1719.2
## - test_prep:transport_means               1     17.85 5636.6 1719.6
## <none>                                                5618.8 1719.7
## - test_prep:wkly_study_hours              2     38.99 5657.8 1719.8
## - test_prep:practice_sport                2     39.70 5658.5 1719.9
## - writing_score:math_score                1     21.31 5640.1 1719.9
## - lunch_type:practice_sport               2     42.28 5661.1 1720.1
## - lunch_type:writing_score                1     26.65 5645.4 1720.5
## - is_first_child:transport_means          1     29.62 5648.4 1720.8
## - practice_sport:is_first_child           2     49.76 5668.5 1720.9
## - test_prep:parent_marital_status         2     50.29 5669.1 1721.0
## - lunch_type:wkly_study_hours             2     52.61 5671.4 1721.2
## - parent_marital_status:is_first_child    2     52.99 5671.8 1721.2
## - practice_sport:writing_score            2     58.82 5677.6 1721.9
## + parent_educ:transport_means             5     73.94 5544.8 1721.9
## + is_first_child:wkly_study_hours         2     16.30 5602.5 1722.0
## + ethnic_group:test_prep                  4     52.20 5566.6 1722.2
## - parent_educ:math_score                  5    120.87 5739.7 1722.3
## + parent_marital_status:transport_means   2     11.51 5607.3 1722.5
## - gender:math_score                       1     45.81 5664.6 1722.5
## - gender:practice_sport                   2     65.10 5683.9 1722.5
## - test_prep:is_first_child                1     46.36 5665.1 1722.6
## - ethnic_group:transport_means            4    106.47 5725.3 1722.8
## - parent_educ:test_prep                   5    126.73 5745.5 1722.9
## - gender:writing_score                    1     51.73 5670.5 1723.1
## - lunch_type:parent_marital_status        3     91.10 5709.9 1723.2
## + parent_marital_status:math_score        2      4.77 5614.0 1723.2
## - wkly_study_hours:math_score             2     75.00 5693.8 1723.5
## - gender:wkly_study_hours                 2     75.34 5694.1 1723.6
## + practice_sport:wkly_study_hours         4     39.19 5579.6 1723.6
## - parent_marital_status:writing_score     3     96.44 5715.2 1723.8
## - parent_educ:practice_sport             10    237.94 5856.7 1724.2
## + parent_marital_status:practice_sport    4     33.25 5585.5 1724.2
## + ethnic_group:is_first_child             4     31.89 5586.9 1724.3
## - wkly_study_hours:writing_score          2     86.03 5704.8 1724.7
## - practice_sport:math_score               2     86.82 5705.6 1724.8
## - ethnic_group:wkly_study_hours           8    204.46 5823.2 1724.8
## + parent_educ:writing_score               5     40.28 5578.5 1725.5
## + gender:ethnic_group                     4      5.99 5612.8 1727.1
## + ethnic_group:math_score                 4      3.53 5615.3 1727.3
## + parent_educ:lunch_type                  5     17.71 5601.1 1727.8
## + parent_educ:wkly_study_hours           10    104.72 5514.1 1728.6
## - parent_marital_status:wkly_study_hours  5    200.09 5818.9 1730.4
## - ethnic_group:parent_educ               20    545.75 6164.5 1734.4
## - ethnic_group:lunch_type                 4    234.14 5852.9 1735.8
## - ethnic_group:writing_score              4    237.08 5855.9 1736.1
## - ethnic_group:parent_marital_status     10    432.17 6051.0 1743.4
## 
## Step:  AIC=1717.02
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - parent_educ:is_first_child              5     76.61 5707.8 1715.0
## - gender:transport_means                  1      0.02 5631.2 1715.0
## - test_prep:writing_score                 1      0.05 5631.3 1715.0
## - lunch_type:transport_means              1      0.39 5631.6 1715.1
## - transport_means:math_score              1      0.41 5631.6 1715.1
## - is_first_child:writing_score            1      0.55 5631.8 1715.1
## - gender:is_first_child                   1      0.58 5631.8 1715.1
## - transport_means:wkly_study_hours        2     19.72 5650.9 1715.1
## - lunch_type:is_first_child               1      0.65 5631.9 1715.1
## - test_prep:math_score                    1      1.28 5632.5 1715.2
## - gender:parent_educ                      5     78.20 5709.4 1715.2
## - gender:test_prep                        1      1.52 5632.7 1715.2
## - is_first_child:math_score               1      2.54 5633.8 1715.3
## - ethnic_group:practice_sport             8    139.44 5770.7 1715.5
## - gender:parent_marital_status            3     44.60 5675.8 1715.7
## - transport_means:writing_score           1      8.58 5639.8 1715.9
## - gender:lunch_type                       1     10.13 5641.4 1716.1
## - lunch_type:math_score                   1     10.99 5642.2 1716.2
## - test_prep:transport_means               1     15.79 5647.0 1716.7
## - parent_educ:parent_marital_status      14    271.11 5902.3 1716.8
## - lunch_type:test_prep                    1     16.94 5648.2 1716.8
## - test_prep:wkly_study_hours              2     37.83 5669.0 1717.0
## <none>                                                5631.2 1717.0
## - test_prep:practice_sport                2     40.42 5671.6 1717.2
## - writing_score:math_score                1     21.75 5653.0 1717.3
## - lunch_type:practice_sport               2     42.95 5674.2 1717.5
## - practice_sport:is_first_child           2     45.77 5677.0 1717.8
## - lunch_type:writing_score                1     26.71 5657.9 1717.8
## - test_prep:parent_marital_status         2     51.42 5682.6 1718.4
## - practice_sport:writing_score            2     52.61 5683.8 1718.5
## - is_first_child:transport_means          1     35.50 5666.7 1718.7
## - lunch_type:wkly_study_hours             2     55.18 5686.4 1718.8
## - parent_marital_status:is_first_child    2     56.95 5688.2 1719.0
## - gender:practice_sport                   2     59.72 5690.9 1719.2
## + is_first_child:wkly_study_hours         2     14.80 5616.4 1719.5
## + ethnic_group:test_prep                  4     52.63 5578.6 1719.5
## - test_prep:is_first_child                1     43.24 5674.5 1719.5
## + parent_marital_status:transport_means   2     13.34 5617.9 1719.6
## + practice_sport:transport_means          2     12.44 5618.8 1719.7
## - gender:math_score                       1     46.07 5677.3 1719.8
## - parent_educ:math_score                  5    123.58 5754.8 1719.8
## + parent_educ:transport_means             5     67.71 5563.5 1719.9
## - ethnic_group:transport_means            4    106.18 5737.4 1720.0
## - parent_educ:test_prep                   5    126.08 5757.3 1720.1
## - gender:writing_score                    1     50.52 5681.7 1720.3
## - lunch_type:parent_marital_status        3     89.48 5720.7 1720.3
## + parent_marital_status:math_score        2      5.67 5625.6 1720.4
## - wkly_study_hours:math_score             2     72.34 5703.6 1720.5
## - gender:wkly_study_hours                 2     73.01 5704.2 1720.6
## - parent_marital_status:writing_score     3     94.41 5725.6 1720.8
## + practice_sport:wkly_study_hours         4     39.22 5592.0 1720.9
## - practice_sport:math_score               2     78.17 5709.4 1721.2
## - wkly_study_hours:writing_score          2     82.68 5713.9 1721.6
## + parent_marital_status:practice_sport    4     32.00 5599.2 1721.7
## + ethnic_group:is_first_child             4     31.24 5600.0 1721.7
## - ethnic_group:wkly_study_hours           8    204.12 5835.3 1722.0
## + parent_educ:writing_score               5     39.07 5592.2 1722.9
## - parent_educ:practice_sport             10    263.04 5894.3 1724.0
## + gender:ethnic_group                     4      6.02 5625.2 1724.4
## + ethnic_group:math_score                 4      3.58 5627.6 1724.6
## + parent_educ:lunch_type                  5     17.31 5613.9 1725.2
## + parent_educ:wkly_study_hours           10    106.46 5524.8 1725.8
## - parent_marital_status:wkly_study_hours  5    211.62 5842.8 1728.8
## - ethnic_group:writing_score              4    230.12 5861.3 1732.7
## - ethnic_group:lunch_type                 4    232.75 5864.0 1732.9
## - ethnic_group:parent_educ               20    561.30 6192.5 1733.1
## - ethnic_group:parent_marital_status     10    438.60 6069.8 1741.3
## 
## Step:  AIC=1714.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:transport_means                  1      0.01 5707.8 1713.0
## - test_prep:writing_score                 1      0.15 5708.0 1713.0
## - is_first_child:math_score               1      0.27 5708.1 1713.0
## - transport_means:math_score              1      0.53 5708.4 1713.0
## - is_first_child:writing_score            1      1.29 5709.1 1713.1
## - lunch_type:transport_means              1      1.38 5709.2 1713.1
## - gender:test_prep                        1      1.70 5709.5 1713.2
## - test_prep:math_score                    1      2.61 5710.4 1713.3
## - lunch_type:is_first_child               1      3.12 5711.0 1713.3
## - gender:is_first_child                   1      4.45 5712.3 1713.5
## - transport_means:wkly_study_hours        2     26.24 5734.1 1713.7
## - transport_means:writing_score           1      7.06 5714.9 1713.7
## - ethnic_group:practice_sport             8    146.35 5854.2 1713.9
## - gender:parent_marital_status            3     48.88 5756.7 1714.0
## - lunch_type:math_score                   1     10.29 5718.1 1714.0
## - gender:lunch_type                       1     10.90 5718.7 1714.1
## - test_prep:transport_means               1     12.71 5720.5 1714.3
## - writing_score:math_score                1     16.70 5724.5 1714.7
## - lunch_type:test_prep                    1     17.61 5725.4 1714.8
## - test_prep:wkly_study_hours              2     37.92 5745.8 1714.9
## <none>                                                5707.8 1715.0
## - lunch_type:practice_sport               2     39.42 5747.3 1715.0
## - test_prep:practice_sport                2     39.70 5747.5 1715.1
## - lunch_type:writing_score                1     24.64 5732.5 1715.5
## - practice_sport:is_first_child           2     44.32 5752.2 1715.5
## - practice_sport:writing_score            2     54.68 5762.5 1716.6
## - gender:parent_educ                      5    114.58 5822.4 1716.7
## - gender:math_score                       1     37.43 5745.3 1716.8
## - gender:writing_score                    1     37.56 5745.4 1716.9
## - is_first_child:transport_means          1     38.28 5746.1 1716.9
## + parent_educ:is_first_child              5     76.61 5631.2 1717.0
## - test_prep:parent_marital_status         2     60.46 5768.3 1717.2
## - lunch_type:wkly_study_hours             2     60.62 5768.5 1717.2
## + ethnic_group:test_prep                  4     55.40 5652.4 1717.2
## + parent_marital_status:transport_means   2     15.40 5692.4 1717.4
## - parent_educ:parent_marital_status      14    304.41 6012.2 1717.6
## + is_first_child:wkly_study_hours         2     12.69 5695.1 1717.7
## - ethnic_group:transport_means            4    105.20 5813.0 1717.8
## - gender:practice_sport                   2     66.04 5773.9 1717.8
## + practice_sport:wkly_study_hours         4     49.34 5658.5 1717.9
## + practice_sport:transport_means          2      8.61 5699.2 1718.1
## - parent_marital_status:is_first_child    2     71.31 5779.1 1718.3
## - lunch_type:parent_marital_status        3     90.99 5798.8 1718.3
## - parent_educ:math_score                  5    132.47 5840.3 1718.5
## + parent_educ:transport_means             5     61.88 5646.0 1718.6
## + parent_marital_status:math_score        2      3.43 5704.4 1718.6
## - test_prep:is_first_child                1     58.78 5766.6 1719.0
## - parent_educ:test_prep                   5    138.60 5846.4 1719.1
## - wkly_study_hours:math_score             2     80.15 5788.0 1719.2
## - parent_marital_status:writing_score     3    102.30 5810.1 1719.5
## + parent_marital_status:practice_sport    4     31.21 5676.6 1719.8
## - gender:wkly_study_hours                 2     86.41 5794.2 1719.8
## - practice_sport:math_score               2     86.57 5794.4 1719.9
## + parent_educ:writing_score               5     48.93 5658.9 1719.9
## + ethnic_group:is_first_child             4     25.75 5682.1 1720.3
## - wkly_study_hours:writing_score          2     92.28 5800.1 1720.5
## - ethnic_group:wkly_study_hours           8    215.01 5922.8 1720.8
## + ethnic_group:math_score                 4      7.13 5700.7 1722.2
## + gender:ethnic_group                     4      4.96 5702.9 1722.5
## - parent_educ:practice_sport             10    273.62 5981.5 1722.6
## + parent_educ:lunch_type                  5     16.87 5691.0 1723.2
## + parent_educ:wkly_study_hours           10    110.41 5597.4 1723.5
## - parent_marital_status:wkly_study_hours  5    212.41 5920.2 1726.5
## - ethnic_group:writing_score              4    208.55 5916.4 1728.2
## - ethnic_group:parent_educ               20    559.42 6267.3 1730.2
## - ethnic_group:lunch_type                 4    230.04 5937.9 1730.3
## - ethnic_group:parent_marital_status     10    449.91 6157.7 1739.8
## 
## Step:  AIC=1712.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:wkly_study_hours + gender:writing_score + gender:math_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:writing_score + 
##     is_first_child:math_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:writing_score                 1      0.16 5708.0 1711.0
## - is_first_child:math_score               1      0.26 5708.1 1711.0
## - is_first_child:writing_score            1      1.31 5709.2 1711.1
## - lunch_type:transport_means              1      1.37 5709.2 1711.1
## - transport_means:math_score              1      1.53 5709.4 1711.2
## - gender:test_prep                        1      1.75 5709.6 1711.2
## - test_prep:math_score                    1      2.66 5710.5 1711.3
## - lunch_type:is_first_child               1      3.11 5711.0 1711.3
## - gender:is_first_child                   1      4.45 5712.3 1711.5
## - transport_means:wkly_study_hours        2     26.26 5734.1 1711.7
## - ethnic_group:practice_sport             8    146.97 5854.8 1712.0
## - gender:parent_marital_status            3     48.88 5756.7 1712.0
## - lunch_type:math_score                   1     10.28 5718.1 1712.0
## - gender:lunch_type                       1     10.89 5718.7 1712.1
## - test_prep:transport_means               1     14.07 5721.9 1712.4
## - writing_score:math_score                1     16.70 5724.5 1712.7
## - transport_means:writing_score           1     17.57 5725.4 1712.8
## - lunch_type:test_prep                    1     17.60 5725.4 1712.8
## - test_prep:wkly_study_hours              2     37.92 5745.8 1712.9
## <none>                                                5707.8 1713.0
## - lunch_type:practice_sport               2     39.47 5747.3 1713.1
## - test_prep:practice_sport                2     39.70 5747.5 1713.1
## - lunch_type:writing_score                1     24.66 5732.5 1713.5
## - practice_sport:is_first_child           2     44.37 5752.2 1713.6
## - practice_sport:writing_score            2     54.87 5762.7 1714.6
## - gender:parent_educ                      5    114.61 5822.5 1714.7
## - gender:math_score                       1     37.46 5745.3 1714.8
## - gender:writing_score                    1     37.56 5745.4 1714.9
## - is_first_child:transport_means          1     38.36 5746.2 1714.9
## + gender:transport_means                  1      0.01 5707.8 1715.0
## + parent_educ:is_first_child              5     76.60 5631.2 1715.0
## - test_prep:parent_marital_status         2     60.48 5768.3 1715.2
## - lunch_type:wkly_study_hours             2     60.72 5768.6 1715.2
## + ethnic_group:test_prep                  4     54.54 5653.3 1715.3
## + parent_marital_status:transport_means   2     15.30 5692.5 1715.4
## - parent_educ:parent_marital_status      14    304.60 6012.4 1715.7
## + is_first_child:wkly_study_hours         2     12.67 5695.2 1715.7
## - gender:practice_sport                   2     66.34 5774.2 1715.8
## + practice_sport:wkly_study_hours         4     49.27 5658.6 1715.9
## - ethnic_group:transport_means            4    106.54 5814.4 1715.9
## + practice_sport:transport_means          2      8.58 5699.3 1716.1
## - parent_marital_status:is_first_child    2     71.40 5779.2 1716.3
## - lunch_type:parent_marital_status        3     91.10 5798.9 1716.3
## + parent_educ:transport_means             5     61.87 5646.0 1716.6
## - parent_educ:math_score                  5    133.46 5841.3 1716.6
## + parent_marital_status:math_score        2      3.41 5704.4 1716.6
## - test_prep:is_first_child                1     58.88 5766.7 1717.0
## - parent_educ:test_prep                   5    138.91 5846.8 1717.2
## - wkly_study_hours:math_score             2     80.43 5788.3 1717.2
## - parent_marital_status:writing_score     3    102.30 5810.1 1717.5
## + parent_marital_status:practice_sport    4     31.21 5676.6 1717.8
## - gender:wkly_study_hours                 2     86.68 5794.5 1717.9
## - practice_sport:math_score               2     86.74 5794.6 1717.9
## + parent_educ:writing_score               5     48.93 5658.9 1717.9
## + ethnic_group:is_first_child             4     25.65 5682.2 1718.3
## - wkly_study_hours:writing_score          2     92.59 5800.4 1718.5
## - ethnic_group:wkly_study_hours           8    215.02 5922.9 1718.8
## + ethnic_group:math_score                 4      7.13 5700.7 1720.2
## + gender:ethnic_group                     4      4.95 5702.9 1720.5
## - parent_educ:practice_sport             10    273.79 5981.6 1720.6
## + parent_educ:lunch_type                  5     16.87 5691.0 1721.2
## + parent_educ:wkly_study_hours           10    110.39 5597.5 1721.5
## - parent_marital_status:wkly_study_hours  5    212.46 5920.3 1724.5
## - ethnic_group:writing_score              4    209.20 5917.0 1726.2
## - ethnic_group:parent_educ               20    559.42 6267.3 1728.2
## - ethnic_group:lunch_type                 4    230.06 5937.9 1728.3
## - ethnic_group:parent_marital_status     10    451.07 6158.9 1737.9
## 
## Step:  AIC=1711.01
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:wkly_study_hours + gender:writing_score + gender:math_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + is_first_child:math_score + 
##     transport_means:wkly_study_hours + transport_means:writing_score + 
##     transport_means:math_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - is_first_child:math_score               1      0.24 5708.2 1709.0
## - lunch_type:transport_means              1      1.34 5709.3 1709.1
## - is_first_child:writing_score            1      1.37 5709.4 1709.2
## - transport_means:math_score              1      1.51 5709.5 1709.2
## - gender:test_prep                        1      2.58 5710.6 1709.3
## - lunch_type:is_first_child               1      3.11 5711.1 1709.3
## - gender:is_first_child                   1      4.48 5712.5 1709.5
## - transport_means:wkly_study_hours        2     26.18 5734.2 1709.7
## - test_prep:math_score                    1      8.18 5716.2 1709.8
## - gender:parent_marital_status            3     48.73 5756.7 1710.0
## - ethnic_group:practice_sport             8    147.33 5855.3 1710.0
## - lunch_type:math_score                   1     10.57 5718.6 1710.1
## - gender:lunch_type                       1     11.37 5719.4 1710.2
## - test_prep:transport_means               1     13.97 5722.0 1710.5
## - writing_score:math_score                1     16.90 5724.9 1710.8
## - lunch_type:test_prep                    1     17.52 5725.5 1710.8
## - transport_means:writing_score           1     17.77 5725.8 1710.8
## - test_prep:wkly_study_hours              2     37.81 5745.8 1710.9
## <none>                                                5708.0 1711.0
## - test_prep:practice_sport                2     39.84 5747.8 1711.1
## - lunch_type:practice_sport               2     39.86 5747.9 1711.1
## - practice_sport:is_first_child           2     44.42 5752.4 1711.6
## - lunch_type:writing_score                1     25.50 5733.5 1711.6
## - practice_sport:writing_score            2     54.91 5762.9 1712.7
## - gender:math_score                       1     37.35 5745.4 1712.8
## - gender:writing_score                    1     37.43 5745.4 1712.9
## - gender:parent_educ                      5    116.10 5824.1 1712.9
## - is_first_child:transport_means          1     38.50 5746.5 1713.0
## + test_prep:writing_score                 1      0.16 5707.8 1713.0
## + gender:transport_means                  1      0.02 5708.0 1713.0
## + parent_educ:is_first_child              5     76.71 5631.3 1713.0
## - test_prep:parent_marital_status         2     60.42 5768.4 1713.2
## - lunch_type:wkly_study_hours             2     60.56 5768.6 1713.2
## + ethnic_group:test_prep                  4     54.69 5653.3 1713.3
## + parent_marital_status:transport_means   2     15.18 5692.8 1713.4
## + is_first_child:wkly_study_hours         2     12.71 5695.3 1713.7
## - gender:practice_sport                   2     66.77 5774.8 1713.9
## - parent_educ:parent_marital_status      14    306.63 6014.6 1713.9
## + practice_sport:wkly_study_hours         4     49.28 5658.7 1713.9
## - ethnic_group:transport_means            4    106.39 5814.4 1713.9
## + practice_sport:transport_means          2      8.70 5699.3 1714.1
## - parent_marital_status:is_first_child    2     71.25 5779.3 1714.3
## - lunch_type:parent_marital_status        3     90.95 5799.0 1714.3
## + parent_educ:transport_means             5     61.73 5646.3 1714.6
## + parent_marital_status:math_score        2      3.26 5704.7 1714.7
## - parent_educ:math_score                  5    133.91 5841.9 1714.7
## - test_prep:is_first_child                1     58.77 5766.8 1715.0
## - parent_educ:test_prep                   5    138.87 5846.9 1715.2
## - wkly_study_hours:math_score             2     80.27 5788.3 1715.2
## - parent_marital_status:writing_score     3    102.59 5810.6 1715.5
## + parent_marital_status:practice_sport    4     30.77 5677.2 1715.8
## - gender:wkly_study_hours                 2     86.54 5794.5 1715.9
## - practice_sport:math_score               2     86.86 5794.9 1715.9
## + parent_educ:writing_score               5     47.96 5660.0 1716.0
## + ethnic_group:is_first_child             4     25.80 5682.2 1716.3
## - wkly_study_hours:writing_score          2     92.44 5800.4 1716.5
## - ethnic_group:wkly_study_hours           8    214.87 5922.9 1716.8
## + ethnic_group:math_score                 4      7.12 5700.9 1718.3
## + gender:ethnic_group                     4      4.92 5703.1 1718.5
## - parent_educ:practice_sport             10    274.10 5982.1 1718.7
## + parent_educ:lunch_type                  5     17.03 5691.0 1719.2
## + parent_educ:wkly_study_hours           10    109.64 5598.4 1719.6
## - parent_marital_status:wkly_study_hours  5    212.84 5920.8 1722.6
## - ethnic_group:writing_score              4    209.86 5917.9 1724.3
## - ethnic_group:parent_educ               20    559.78 6267.8 1726.2
## - ethnic_group:lunch_type                 4    229.91 5937.9 1726.3
## - ethnic_group:parent_marital_status     10    451.90 6159.9 1736.0
## 
## Step:  AIC=1709.03
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:wkly_study_hours + gender:writing_score + gender:math_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:transport_means              1      1.27 5709.5 1707.2
## - transport_means:math_score              1      1.56 5709.8 1707.2
## - gender:test_prep                        1      2.56 5710.8 1707.3
## - lunch_type:is_first_child               1      2.89 5711.1 1707.3
## - transport_means:wkly_study_hours        2     26.35 5734.6 1707.8
## - test_prep:math_score                    1      8.05 5716.3 1707.9
## - gender:parent_marital_status            3     48.53 5756.8 1708.0
## - ethnic_group:practice_sport             8    147.30 5855.5 1708.1
## - lunch_type:math_score                   1     10.42 5718.7 1708.1
## - gender:lunch_type                       1     11.23 5719.5 1708.2
## - test_prep:transport_means               1     13.88 5722.1 1708.5
## - gender:is_first_child                   1     13.91 5722.2 1708.5
## - is_first_child:writing_score            1     16.29 5724.5 1708.7
## - writing_score:math_score                1     16.93 5725.2 1708.8
## - transport_means:writing_score           1     17.54 5725.8 1708.8
## - lunch_type:test_prep                    1     17.55 5725.8 1708.8
## - test_prep:wkly_study_hours              2     38.73 5747.0 1709.0
## <none>                                                5708.2 1709.0
## - lunch_type:practice_sport               2     39.87 5748.1 1709.1
## - test_prep:practice_sport                2     39.91 5748.1 1709.1
## - lunch_type:writing_score                1     25.27 5733.5 1709.6
## - practice_sport:is_first_child           2     45.31 5753.5 1709.7
## - practice_sport:writing_score            2     55.07 5763.3 1710.7
## - gender:math_score                       1     37.12 5745.4 1710.9
## - gender:writing_score                    1     37.27 5745.5 1710.9
## - gender:parent_educ                      5    116.14 5824.4 1710.9
## - is_first_child:transport_means          1     38.45 5746.7 1711.0
## + is_first_child:math_score               1      0.24 5708.0 1711.0
## + test_prep:writing_score                 1      0.13 5708.1 1711.0
## + gender:transport_means                  1      0.01 5708.2 1711.0
## - test_prep:parent_marital_status         2     60.18 5768.4 1711.2
## - lunch_type:wkly_study_hours             2     60.64 5768.9 1711.3
## + parent_educ:is_first_child              5     74.37 5633.9 1711.3
## + ethnic_group:test_prep                  4     54.48 5653.8 1711.4
## + parent_marital_status:transport_means   2     14.94 5693.3 1711.5
## + is_first_child:wkly_study_hours         2     12.16 5696.1 1711.8
## - parent_educ:parent_marital_status      14    306.48 6014.7 1711.9
## - gender:practice_sport                   2     66.78 5775.0 1711.9
## + practice_sport:wkly_study_hours         4     47.93 5660.3 1712.1
## + practice_sport:transport_means          2      8.91 5699.3 1712.1
## - ethnic_group:transport_means            4    108.26 5816.5 1712.1
## - parent_marital_status:is_first_child    2     71.06 5779.3 1712.3
## - lunch_type:parent_marital_status        3     90.83 5799.1 1712.3
## + parent_educ:transport_means             5     61.90 5646.3 1712.6
## + parent_marital_status:math_score        2      3.24 5705.0 1712.7
## - parent_educ:math_score                  5    134.51 5842.7 1712.8
## - parent_educ:test_prep                   5    139.45 5847.7 1713.3
## - wkly_study_hours:math_score             2     82.11 5790.4 1713.5
## - parent_marital_status:writing_score     3    102.40 5810.6 1713.5
## - test_prep:is_first_child                1     65.12 5773.4 1713.7
## + parent_marital_status:practice_sport    4     30.99 5677.2 1713.8
## - gender:wkly_study_hours                 2     86.99 5795.2 1714.0
## - practice_sport:math_score               2     87.20 5795.4 1714.0
## + parent_educ:writing_score               5     47.21 5661.0 1714.1
## + ethnic_group:is_first_child             4     24.50 5683.7 1714.5
## - wkly_study_hours:writing_score          2     94.32 5802.6 1714.7
## - ethnic_group:wkly_study_hours           8    214.85 5923.1 1714.8
## + ethnic_group:math_score                 4      7.13 5701.1 1716.3
## + gender:ethnic_group                     4      5.03 5703.2 1716.5
## - parent_educ:practice_sport             10    274.38 5982.6 1716.7
## + parent_educ:lunch_type                  5     16.79 5691.4 1717.3
## + parent_educ:wkly_study_hours           10    109.61 5598.6 1717.6
## - parent_marital_status:wkly_study_hours  5    212.67 5920.9 1720.6
## - ethnic_group:writing_score              4    212.01 5920.3 1722.5
## - ethnic_group:parent_educ               20    559.64 6267.9 1724.2
## - ethnic_group:lunch_type                 4    233.97 5942.2 1724.7
## - ethnic_group:parent_marital_status     10    452.36 6160.6 1734.0
## 
## Step:  AIC=1707.16
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:wkly_study_hours + gender:writing_score + gender:math_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     lunch_type:writing_score + lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:test_prep                        1      2.50 5712.0 1705.4
## - lunch_type:is_first_child               1      2.78 5712.3 1705.5
## - transport_means:math_score              1      2.84 5712.4 1705.5
## - transport_means:wkly_study_hours        2     25.63 5735.1 1705.8
## - test_prep:math_score                    1      8.28 5717.8 1706.0
## - gender:parent_marital_status            3     47.94 5757.5 1706.1
## - lunch_type:math_score                   1     11.12 5720.6 1706.3
## - gender:lunch_type                       1     11.97 5721.5 1706.4
## - ethnic_group:practice_sport             8    149.83 5859.3 1706.5
## - gender:is_first_child                   1     14.49 5724.0 1706.7
## - test_prep:transport_means               1     15.10 5724.6 1706.7
## - is_first_child:writing_score            1     16.70 5726.2 1706.9
## - transport_means:writing_score           1     17.00 5726.5 1706.9
## - writing_score:math_score                1     17.08 5726.6 1706.9
## - test_prep:wkly_study_hours              2     37.84 5747.4 1707.1
## - lunch_type:test_prep                    1     19.32 5728.8 1707.2
## <none>                                                5709.5 1707.2
## - lunch_type:practice_sport               2     38.96 5748.5 1707.2
## - test_prep:practice_sport                2     40.26 5749.8 1707.3
## - lunch_type:writing_score                1     26.73 5736.2 1707.9
## - practice_sport:is_first_child           2     46.41 5755.9 1707.9
## - practice_sport:writing_score            2     54.80 5764.3 1708.8
## - gender:math_score                       1     37.01 5746.5 1709.0
## - gender:writing_score                    1     37.23 5746.7 1709.0
## + lunch_type:transport_means              1      1.27 5708.2 1709.0
## - gender:parent_educ                      5    116.89 5826.4 1709.1
## + is_first_child:math_score               1      0.17 5709.3 1709.1
## - is_first_child:transport_means          1     38.68 5748.2 1709.2
## + test_prep:writing_score                 1      0.10 5709.4 1709.2
## + gender:transport_means                  1      0.00 5709.5 1709.2
## - lunch_type:wkly_study_hours             2     59.93 5769.4 1709.3
## + parent_educ:is_first_child              5     75.35 5634.2 1709.3
## - test_prep:parent_marital_status         2     60.38 5769.9 1709.4
## + ethnic_group:test_prep                  4     55.14 5654.4 1709.4
## + parent_marital_status:transport_means   2     15.29 5694.2 1709.6
## + is_first_child:wkly_study_hours         2     11.86 5697.7 1709.9
## - gender:practice_sport                   2     66.17 5775.7 1710.0
## - parent_educ:parent_marital_status      14    306.45 6016.0 1710.0
## + practice_sport:transport_means          2      8.80 5700.7 1710.2
## + practice_sport:wkly_study_hours         4     47.07 5662.5 1710.3
## - ethnic_group:transport_means            4    109.95 5819.5 1710.4
## - parent_marital_status:is_first_child    2     70.69 5780.2 1710.4
## - lunch_type:parent_marital_status        3     90.46 5800.0 1710.4
## + parent_educ:transport_means             5     62.67 5646.8 1710.7
## + parent_marital_status:math_score        2      3.31 5706.2 1710.8
## - parent_educ:math_score                  5    134.15 5843.7 1710.9
## - parent_educ:test_prep                   5    138.88 5848.4 1711.3
## - parent_marital_status:writing_score     3    101.48 5811.0 1711.6
## - wkly_study_hours:math_score             2     81.94 5791.5 1711.6
## - test_prep:is_first_child                1     64.23 5773.7 1711.8
## - practice_sport:math_score               2     86.85 5796.4 1712.1
## + parent_marital_status:practice_sport    4     29.72 5679.8 1712.1
## - gender:wkly_study_hours                 2     88.48 5798.0 1712.2
## + parent_educ:writing_score               5     46.11 5663.4 1712.4
## + ethnic_group:is_first_child             4     23.04 5686.5 1712.8
## - wkly_study_hours:writing_score          2     94.11 5803.6 1712.8
## - ethnic_group:wkly_study_hours           8    215.19 5924.7 1713.0
## + ethnic_group:math_score                 4      6.61 5702.9 1714.5
## + gender:ethnic_group                     4      4.79 5704.7 1714.7
## - parent_educ:practice_sport             10    274.23 5983.7 1714.8
## + parent_educ:lunch_type                  5     16.19 5693.3 1715.5
## + parent_educ:wkly_study_hours           10    109.47 5600.0 1715.7
## - parent_marital_status:wkly_study_hours  5    212.84 5922.4 1718.8
## - ethnic_group:writing_score              4    211.84 5921.4 1720.7
## - ethnic_group:parent_educ               20    558.58 6268.1 1722.2
## - ethnic_group:lunch_type                 4    236.80 5946.3 1723.1
## - ethnic_group:parent_marital_status     10    451.68 6161.2 1732.1
## 
## Step:  AIC=1705.42
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:parent_marital_status + 
##     gender:practice_sport + gender:is_first_child + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:wkly_study_hours + 
##     lunch_type:writing_score + lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:is_first_child               1      2.84 5714.9 1703.7
## - transport_means:math_score              1      3.03 5715.0 1703.7
## - test_prep:math_score                    1      6.98 5719.0 1704.1
## - transport_means:wkly_study_hours        2     26.80 5738.8 1704.2
## - gender:parent_marital_status            3     46.58 5758.6 1704.2
## - ethnic_group:practice_sport             8    148.56 5860.6 1704.6
## - lunch_type:math_score                   1     11.75 5723.8 1704.6
## - gender:lunch_type                       1     12.87 5724.9 1704.8
## - test_prep:transport_means               1     14.19 5726.2 1704.9
## - gender:is_first_child                   1     15.18 5727.2 1705.0
## - is_first_child:writing_score            1     15.63 5727.6 1705.0
## - transport_means:writing_score           1     15.83 5727.8 1705.0
## - writing_score:math_score                1     16.71 5728.7 1705.1
## - test_prep:wkly_study_hours              2     37.24 5749.3 1705.3
## - lunch_type:test_prep                    1     19.35 5731.4 1705.4
## <none>                                                5712.0 1705.4
## - lunch_type:practice_sport               2     39.44 5751.5 1705.5
## - test_prep:practice_sport                2     40.84 5752.9 1705.6
## - practice_sport:is_first_child           2     45.55 5757.6 1706.1
## - lunch_type:writing_score                1     27.38 5739.4 1706.2
## - gender:math_score                       1     34.55 5746.6 1707.0
## - gender:writing_score                    1     35.43 5747.4 1707.1
## + gender:test_prep                        1      2.50 5709.5 1707.2
## - practice_sport:writing_score            2     56.35 5768.4 1707.2
## + lunch_type:transport_means              1      1.22 5710.8 1707.3
## + test_prep:writing_score                 1      1.04 5711.0 1707.3
## + is_first_child:math_score               1      0.15 5711.9 1707.4
## - is_first_child:transport_means          1     38.76 5750.8 1707.4
## + gender:transport_means                  1      0.00 5712.0 1707.4
## - lunch_type:wkly_study_hours             2     59.20 5771.2 1707.5
## - test_prep:parent_marital_status         2     61.22 5773.2 1707.7
## + ethnic_group:test_prep                  4     54.09 5657.9 1707.8
## + parent_educ:is_first_child              5     72.95 5639.1 1707.8
## + parent_marital_status:transport_means   2     15.13 5696.9 1707.9
## + is_first_child:wkly_study_hours         2     12.52 5699.5 1708.1
## - gender:parent_educ                      5    124.76 5836.8 1708.2
## - parent_educ:parent_marital_status      14    306.07 6018.1 1708.2
## - gender:practice_sport                   2     68.26 5780.3 1708.4
## - ethnic_group:transport_means            4    108.07 5820.1 1708.5
## + practice_sport:transport_means          2      8.95 5703.1 1708.5
## + practice_sport:wkly_study_hours         4     47.13 5664.9 1708.5
## - lunch_type:parent_marital_status        3     89.56 5801.6 1708.6
## - parent_marital_status:is_first_child    2     70.66 5782.7 1708.7
## + parent_educ:transport_means             5     62.18 5649.8 1709.0
## - parent_educ:math_score                  5    133.12 5845.1 1709.0
## + parent_marital_status:math_score        2      3.61 5708.4 1709.0
## - parent_educ:test_prep                   5    136.79 5848.8 1709.4
## - wkly_study_hours:math_score             2     81.75 5793.8 1709.8
## - parent_marital_status:writing_score     3    101.48 5813.5 1709.8
## - test_prep:is_first_child                1     63.56 5775.6 1710.0
## + parent_marital_status:practice_sport    4     31.08 5680.9 1710.2
## - gender:wkly_study_hours                 2     86.70 5798.7 1710.3
## - practice_sport:math_score               2     88.67 5800.7 1710.5
## + parent_educ:writing_score               5     45.71 5666.3 1710.7
## - ethnic_group:wkly_study_hours           8    213.02 5925.0 1711.0
## - wkly_study_hours:writing_score          2     93.73 5805.7 1711.0
## + ethnic_group:is_first_child             4     22.69 5689.3 1711.1
## + ethnic_group:math_score                 4      6.58 5705.4 1712.7
## - parent_educ:practice_sport             10    272.20 5984.2 1712.9
## + gender:ethnic_group                     4      4.81 5707.2 1712.9
## + parent_educ:lunch_type                  5     16.44 5695.6 1713.7
## + parent_educ:wkly_study_hours           10    109.72 5602.3 1714.0
## - parent_marital_status:wkly_study_hours  5    210.97 5923.0 1716.8
## - ethnic_group:writing_score              4    209.90 5921.9 1718.7
## - ethnic_group:parent_educ               20    556.08 6268.1 1720.2
## - ethnic_group:lunch_type                 4    235.35 5947.4 1721.2
## - ethnic_group:parent_marital_status     10    452.96 6165.0 1730.4
## 
## Step:  AIC=1703.71
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:parent_marital_status + 
##     gender:practice_sport + gender:is_first_child + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + transport_means:math_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - transport_means:math_score              1      3.31 5718.2 1702.1
## - test_prep:math_score                    1      6.49 5721.4 1702.4
## - gender:parent_marital_status            3     45.57 5760.4 1702.4
## - transport_means:wkly_study_hours        2     26.72 5741.6 1702.5
## - lunch_type:math_score                   1     11.97 5726.8 1703.0
## - is_first_child:writing_score            1     12.96 5727.8 1703.0
## - gender:is_first_child                   1     13.40 5728.3 1703.1
## - ethnic_group:practice_sport             8    151.20 5866.1 1703.1
## - gender:lunch_type                       1     13.91 5728.8 1703.2
## - test_prep:transport_means               1     14.91 5729.8 1703.2
## - transport_means:writing_score           1     15.21 5730.1 1703.3
## - test_prep:wkly_study_hours              2     35.26 5750.1 1703.3
## - writing_score:math_score                1     17.45 5732.3 1703.5
## - lunch_type:practice_sport               2     36.95 5751.8 1703.5
## - lunch_type:test_prep                    1     18.70 5733.6 1703.6
## <none>                                                5714.9 1703.7
## - test_prep:practice_sport                2     40.94 5755.8 1703.9
## - practice_sport:is_first_child           2     47.23 5762.1 1704.6
## - lunch_type:writing_score                1     28.29 5743.1 1704.6
## - gender:math_score                       1     35.40 5750.3 1705.4
## + lunch_type:is_first_child               1      2.84 5712.0 1705.4
## - gender:writing_score                    1     36.05 5750.9 1705.4
## + gender:test_prep                        1      2.57 5712.3 1705.5
## - practice_sport:writing_score            2     56.41 5771.3 1705.5
## + lunch_type:transport_means              1      1.10 5713.8 1705.6
## + test_prep:writing_score                 1      1.05 5713.8 1705.6
## + is_first_child:math_score               1      0.00 5714.9 1705.7
## + gender:transport_means                  1      0.00 5714.9 1705.7
## - is_first_child:transport_means          1     39.57 5754.4 1705.8
## - lunch_type:wkly_study_hours             2     59.29 5774.2 1705.8
## + parent_educ:is_first_child              5     75.45 5639.4 1705.9
## + ethnic_group:test_prep                  4     55.41 5659.4 1706.0
## - test_prep:parent_marital_status         2     60.96 5775.8 1706.0
## + parent_marital_status:transport_means   2     15.72 5699.1 1706.1
## - gender:parent_educ                      5    123.30 5838.2 1706.3
## + is_first_child:wkly_study_hours         2     12.27 5702.6 1706.5
## - parent_educ:parent_marital_status      14    307.98 6022.8 1706.7
## + practice_sport:wkly_study_hours         4     47.96 5666.9 1706.7
## - gender:practice_sport                   2     68.50 5783.4 1706.7
## - lunch_type:parent_marital_status        3     88.62 5803.5 1706.8
## + practice_sport:transport_means          2      8.38 5706.5 1706.8
## - ethnic_group:transport_means            4    110.51 5825.4 1707.0
## - parent_marital_status:is_first_child    2     71.22 5786.1 1707.0
## + parent_marital_status:math_score        2      4.22 5710.6 1707.3
## + parent_educ:transport_means             5     60.92 5653.9 1707.4
## - parent_educ:math_score                  5    137.35 5852.2 1707.7
## - parent_educ:test_prep                   5    139.11 5854.0 1707.9
## - parent_marital_status:writing_score     3    100.18 5815.0 1708.0
## - wkly_study_hours:math_score             2     80.72 5795.6 1708.0
## - test_prep:is_first_child                1     61.15 5776.0 1708.0
## - gender:wkly_study_hours                 2     85.99 5800.9 1708.5
## - practice_sport:math_score               2     88.58 5803.4 1708.8
## + parent_marital_status:practice_sport    4     28.12 5686.7 1708.8
## + parent_educ:writing_score               5     45.03 5669.8 1709.0
## - wkly_study_hours:writing_score          2     92.63 5807.5 1709.2
## + ethnic_group:is_first_child             4     23.28 5691.6 1709.3
## - ethnic_group:wkly_study_hours           8    214.37 5929.2 1709.4
## + ethnic_group:math_score                 4      6.01 5708.9 1711.1
## - parent_educ:practice_sport             10    271.85 5986.7 1711.1
## + gender:ethnic_group                     4      4.25 5710.6 1711.3
## + parent_educ:lunch_type                  5     17.81 5697.0 1711.9
## + parent_educ:wkly_study_hours           10    107.72 5607.1 1712.5
## - parent_marital_status:wkly_study_hours  5    213.17 5928.0 1715.3
## - ethnic_group:writing_score              4    209.35 5924.2 1716.9
## - ethnic_group:lunch_type                 4    232.72 5947.6 1719.3
## - ethnic_group:parent_educ               20    571.04 6285.9 1719.9
## - ethnic_group:parent_marital_status     10    450.33 6165.2 1728.5
## 
## Step:  AIC=1702.06
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:parent_marital_status + 
##     gender:practice_sport + gender:is_first_child + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:math_score                    1      6.45 5724.6 1700.7
## - transport_means:wkly_study_hours        2     26.29 5744.5 1700.8
## - gender:parent_marital_status            3     46.63 5764.8 1700.8
## - lunch_type:math_score                   1     12.40 5730.6 1701.3
## - ethnic_group:practice_sport             8    150.61 5868.8 1701.4
## - is_first_child:writing_score            1     13.49 5731.7 1701.5
## - gender:is_first_child                   1     14.07 5732.2 1701.5
## - gender:lunch_type                       1     14.68 5732.8 1701.6
## - test_prep:wkly_study_hours              2     34.34 5752.5 1701.6
## - test_prep:transport_means               1     16.61 5734.8 1701.8
## - writing_score:math_score                1     16.82 5735.0 1701.8
## - lunch_type:practice_sport               2     37.96 5756.1 1702.0
## - lunch_type:test_prep                    1     19.36 5737.5 1702.0
## <none>                                                5718.2 1702.1
## - test_prep:practice_sport                2     41.77 5759.9 1702.3
## - practice_sport:is_first_child           2     47.31 5765.5 1702.9
## - lunch_type:writing_score                1     29.04 5747.2 1703.0
## + transport_means:math_score              1      3.31 5714.9 1703.7
## + lunch_type:is_first_child               1      3.12 5715.0 1703.7
## + gender:test_prep                        1      2.77 5715.4 1703.8
## - gender:math_score                       1     36.26 5754.4 1703.8
## + lunch_type:transport_means              1      2.44 5715.7 1703.8
## + gender:transport_means                  1      1.83 5716.3 1703.9
## - gender:writing_score                    1     37.41 5755.6 1703.9
## + test_prep:writing_score                 1      1.24 5716.9 1703.9
## - is_first_child:transport_means          1     37.69 5755.9 1703.9
## + is_first_child:math_score               1      0.01 5718.2 1704.0
## + parent_educ:is_first_child              5     76.24 5641.9 1704.1
## + ethnic_group:test_prep                  4     56.41 5661.8 1704.2
## - test_prep:parent_marital_status         2     59.94 5778.1 1704.2
## - practice_sport:writing_score            2     60.20 5778.4 1704.2
## - gender:parent_educ                      5    121.03 5839.2 1704.4
## - lunch_type:wkly_study_hours             2     62.71 5780.9 1704.5
## + parent_marital_status:transport_means   2     14.71 5703.5 1704.5
## + is_first_child:wkly_study_hours         2     12.24 5705.9 1704.8
## - lunch_type:parent_marital_status        3     87.22 5805.4 1705.0
## + practice_sport:wkly_study_hours         4     48.44 5669.7 1705.0
## - parent_educ:parent_marital_status      14    308.43 6026.6 1705.0
## - ethnic_group:transport_means            4    108.05 5826.2 1705.1
## - gender:practice_sport                   2     69.54 5787.7 1705.2
## + practice_sport:transport_means          2      8.27 5709.9 1705.2
## - parent_marital_status:is_first_child    2     72.87 5791.0 1705.5
## + parent_marital_status:math_score        2      4.53 5713.6 1705.6
## + parent_educ:transport_means             5     61.34 5656.8 1705.7
## - parent_educ:math_score                  5    135.34 5853.5 1705.9
## - wkly_study_hours:math_score             2     79.16 5797.3 1706.2
## - test_prep:is_first_child                1     59.72 5777.9 1706.2
## - parent_marital_status:writing_score     3    100.50 5818.7 1706.3
## - parent_educ:test_prep                   5    140.46 5858.6 1706.4
## - gender:wkly_study_hours                 2     84.07 5802.2 1706.7
## + parent_marital_status:practice_sport    4     28.58 5689.6 1707.1
## - wkly_study_hours:writing_score          2     90.49 5808.7 1707.3
## + parent_educ:writing_score               5     44.80 5673.4 1707.4
## - ethnic_group:wkly_study_hours           8    211.87 5930.0 1707.5
## - practice_sport:math_score               2     93.21 5811.4 1707.6
## + ethnic_group:is_first_child             4     23.24 5694.9 1707.7
## - transport_means:writing_score           1     82.71 5800.9 1708.5
## + ethnic_group:math_score                 4      6.00 5712.2 1709.4
## - parent_educ:practice_sport             10    272.14 5990.3 1709.5
## + gender:ethnic_group                     4      4.27 5713.9 1709.6
## + parent_educ:lunch_type                  5     17.32 5700.8 1710.3
## + parent_educ:wkly_study_hours           10    108.38 5609.8 1710.8
## - parent_marital_status:wkly_study_hours  5    215.58 5933.7 1713.9
## - ethnic_group:writing_score              4    209.62 5927.8 1715.3
## - ethnic_group:lunch_type                 4    232.62 5950.8 1717.6
## - ethnic_group:parent_educ               20    579.00 6297.2 1719.0
## - ethnic_group:parent_marital_status     10    454.06 6172.2 1727.1
## 
## Step:  AIC=1700.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:parent_marital_status + 
##     gender:practice_sport + gender:is_first_child + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + transport_means:wkly_study_hours + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - transport_means:wkly_study_hours        2     26.51 5751.1 1699.5
## - gender:parent_marital_status            3     46.82 5771.4 1699.5
## - ethnic_group:practice_sport             8    148.04 5872.7 1699.8
## - writing_score:math_score                1     11.44 5736.1 1699.9
## - test_prep:wkly_study_hours              2     31.43 5756.0 1700.0
## - lunch_type:math_score                   1     13.40 5738.0 1700.1
## - lunch_type:test_prep                    1     13.94 5738.6 1700.2
## - gender:is_first_child                   1     14.87 5739.5 1700.2
## - gender:lunch_type                       1     14.90 5739.5 1700.2
## - is_first_child:writing_score            1     15.18 5739.8 1700.3
## - test_prep:transport_means               1     15.71 5740.3 1700.3
## - lunch_type:practice_sport               2     37.53 5762.1 1700.6
## <none>                                                5724.6 1700.7
## - test_prep:practice_sport                2     43.50 5768.1 1701.2
## - lunch_type:writing_score                1     27.72 5752.3 1701.6
## - practice_sport:is_first_child           2     50.17 5774.8 1701.9
## + test_prep:writing_score                 1      7.01 5717.6 1702.0
## + test_prep:math_score                    1      6.45 5718.2 1702.1
## + transport_means:math_score              1      3.26 5721.4 1702.4
## + ethnic_group:test_prep                  4     60.91 5663.7 1702.4
## + lunch_type:transport_means              1      2.74 5721.9 1702.4
## + lunch_type:is_first_child               1      2.61 5722.0 1702.5
## + gender:transport_means                  1      1.88 5722.7 1702.5
## + gender:test_prep                        1      1.42 5723.2 1702.6
## - is_first_child:transport_means          1     37.83 5762.4 1702.6
## - gender:math_score                       1     38.25 5762.9 1702.7
## - practice_sport:writing_score            2     58.01 5782.6 1702.7
## + is_first_child:math_score               1      0.00 5724.6 1702.7
## - gender:parent_educ                      5    118.65 5843.3 1702.8
## + parent_educ:is_first_child              5     76.04 5648.6 1702.8
## - gender:writing_score                    1     41.03 5765.6 1702.9
## - test_prep:parent_marital_status         2     61.30 5785.9 1703.0
## - lunch_type:wkly_study_hours             2     61.51 5786.1 1703.0
## + parent_marital_status:transport_means   2     15.00 5709.6 1703.2
## + is_first_child:wkly_study_hours         2     13.09 5711.5 1703.4
## - parent_educ:parent_marital_status      14    307.01 6031.6 1703.5
## - ethnic_group:transport_means            4    106.75 5831.4 1703.6
## - gender:practice_sport                   2     67.72 5792.3 1703.7
## + practice_sport:wkly_study_hours         4     48.18 5676.4 1703.7
## + practice_sport:transport_means          2      8.89 5715.7 1703.8
## - lunch_type:parent_marital_status        3     90.19 5814.8 1703.9
## - parent_educ:math_score                  5    130.18 5854.8 1704.0
## - parent_marital_status:is_first_child    2     72.21 5796.8 1704.1
## + parent_marital_status:math_score        2      4.28 5720.3 1704.3
## + parent_educ:transport_means             5     60.74 5663.9 1704.4
## - wkly_study_hours:math_score             2     77.63 5802.2 1704.7
## - parent_marital_status:writing_score     3     99.07 5823.7 1704.8
## - parent_educ:test_prep                   5    139.69 5864.3 1704.9
## - test_prep:is_first_child                1     63.06 5787.7 1705.2
## - gender:wkly_study_hours                 2     83.46 5808.1 1705.3
## + parent_marital_status:practice_sport    4     28.55 5696.1 1705.8
## - wkly_study_hours:writing_score          2     89.79 5814.4 1705.9
## + parent_educ:writing_score               5     45.60 5679.0 1706.0
## - ethnic_group:wkly_study_hours           8    210.43 5935.0 1706.0
## - practice_sport:math_score               2     91.36 5816.0 1706.1
## + ethnic_group:is_first_child             4     23.06 5701.6 1706.3
## - transport_means:writing_score           1     78.46 5803.1 1706.8
## + ethnic_group:math_score                 4      6.60 5718.0 1708.0
## + gender:ethnic_group                     4      4.08 5720.5 1708.3
## - parent_educ:practice_sport             10    275.07 5999.7 1708.4
## + parent_educ:lunch_type                  5     19.25 5705.4 1708.7
## + parent_educ:wkly_study_hours           10    107.75 5616.9 1709.5
## - parent_marital_status:wkly_study_hours  5    215.63 5940.2 1712.5
## - ethnic_group:writing_score              4    208.06 5932.7 1713.8
## - ethnic_group:lunch_type                 4    229.78 5954.4 1715.9
## - ethnic_group:parent_educ               20    577.42 6302.0 1717.4
## - ethnic_group:parent_marital_status     10    453.22 6177.8 1725.7
## 
## Step:  AIC=1699.45
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:parent_marital_status + 
##     gender:practice_sport + gender:is_first_child + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + transport_means:writing_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:parent_marital_status            3     45.91 5797.0 1698.1
## - test_prep:wkly_study_hours              2     28.23 5779.4 1698.3
## - writing_score:math_score                1     10.25 5761.4 1698.5
## - lunch_type:test_prep                    1     11.52 5762.6 1698.6
## - ethnic_group:practice_sport             8    151.27 5902.4 1698.8
## - lunch_type:practice_sport               2     34.43 5785.6 1699.0
## - test_prep:transport_means               1     15.21 5766.3 1699.0
## - is_first_child:writing_score            1     15.86 5767.0 1699.1
## - lunch_type:math_score                   1     16.31 5767.4 1699.1
## - gender:lunch_type                       1     16.32 5767.4 1699.1
## - gender:is_first_child                   1     17.15 5768.3 1699.2
## <none>                                                5751.1 1699.5
## - test_prep:practice_sport                2     45.38 5796.5 1700.1
## + test_prep:writing_score                 1      8.38 5742.7 1700.6
## - practice_sport:is_first_child           2     50.93 5802.0 1700.7
## - lunch_type:writing_score                1     31.64 5782.8 1700.7
## + transport_means:wkly_study_hours        2     26.51 5724.6 1700.7
## + test_prep:math_score                    1      6.67 5744.5 1700.8
## + parent_educ:is_first_child              5     81.02 5670.1 1701.1
## - gender:math_score                       1     36.05 5787.2 1701.1
## + transport_means:math_score              1      2.82 5748.3 1701.2
## + lunch_type:is_first_child               1      2.46 5748.7 1701.2
## + gender:test_prep                        1      2.28 5748.8 1701.2
## + gender:transport_means                  1      1.88 5749.2 1701.2
## + lunch_type:transport_means              1      1.54 5749.6 1701.3
## - gender:parent_educ                      5    116.77 5867.9 1701.3
## + is_first_child:math_score               1      0.02 5751.1 1701.4
## - is_first_child:transport_means          1     39.56 5790.7 1701.5
## - test_prep:parent_marital_status         2     59.93 5811.1 1701.6
## - gender:writing_score                    1     40.60 5791.7 1701.6
## - practice_sport:writing_score            2     60.88 5812.0 1701.7
## - lunch_type:wkly_study_hours             2     61.20 5812.3 1701.7
## + parent_marital_status:transport_means   2     15.62 5735.5 1701.8
## + is_first_child:wkly_study_hours         2     15.31 5735.8 1701.9
## + ethnic_group:test_prep                  4     53.67 5697.5 1701.9
## - ethnic_group:transport_means            4    104.97 5856.1 1702.1
## - parent_marital_status:is_first_child    2     68.06 5819.2 1702.4
## - gender:practice_sport                   2     68.88 5820.0 1702.5
## + practice_sport:transport_means          2      8.61 5742.5 1702.6
## - parent_educ:math_score                  5    130.96 5882.1 1702.7
## - wkly_study_hours:math_score             2     72.92 5824.0 1702.9
## + parent_marital_status:math_score        2      5.34 5745.8 1702.9
## + practice_sport:wkly_study_hours         4     43.63 5707.5 1703.0
## + parent_educ:transport_means             5     60.49 5690.6 1703.2
## - parent_educ:test_prep                   5    138.21 5889.3 1703.5
## - gender:wkly_study_hours                 2     78.82 5829.9 1703.5
## - parent_educ:parent_marital_status      14    321.88 6073.0 1703.6
## - test_prep:is_first_child                1     60.63 5811.8 1703.6
## - lunch_type:parent_marital_status        3    100.91 5852.0 1703.7
## - ethnic_group:wkly_study_hours           8    206.24 5957.4 1704.2
## - wkly_study_hours:writing_score          2     87.15 5838.3 1704.3
## + parent_marital_status:practice_sport    4     28.89 5722.2 1704.5
## - parent_marital_status:writing_score     3    109.41 5860.5 1704.6
## - transport_means:writing_score           1     72.46 5823.6 1704.8
## + ethnic_group:is_first_child             4     20.69 5730.4 1705.3
## - parent_educ:practice_sport             10    257.90 6009.0 1705.3
## + parent_educ:writing_score               5     39.90 5711.2 1705.3
## - practice_sport:math_score               2     97.42 5848.5 1705.4
## + ethnic_group:math_score                 4      5.75 5745.4 1706.9
## + gender:ethnic_group                     4      2.79 5748.3 1707.2
## + parent_educ:lunch_type                  5     19.36 5731.8 1707.5
## + parent_educ:wkly_study_hours           10    111.32 5639.8 1707.9
## - parent_marital_status:wkly_study_hours  5    214.49 5965.6 1711.0
## - ethnic_group:writing_score              4    211.92 5963.0 1712.8
## - ethnic_group:lunch_type                 4    222.08 5973.2 1713.8
## - ethnic_group:parent_educ               20    561.71 6312.8 1714.4
## - ethnic_group:parent_marital_status     10    456.45 6207.6 1724.5
## 
## Step:  AIC=1698.14
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     is_first_child:writing_score + transport_means:writing_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:wkly_study_hours              2     23.24 5820.3 1696.5
## - lunch_type:practice_sport               2     30.42 5827.5 1697.2
## - lunch_type:math_score                   1     13.75 5810.8 1697.5
## - test_prep:transport_means               1     15.50 5812.5 1697.7
## - gender:is_first_child                   1     15.59 5812.6 1697.7
## - lunch_type:test_prep                    1     15.98 5813.0 1697.8
## - writing_score:math_score                1     16.00 5813.0 1697.8
## - is_first_child:writing_score            1     16.20 5813.2 1697.8
## - gender:lunch_type                       1     16.43 5813.5 1697.8
## <none>                                                5797.0 1698.1
## - ethnic_group:practice_sport             8    162.19 5959.2 1698.4
## - test_prep:practice_sport                2     44.37 5841.4 1698.6
## - practice_sport:is_first_child           2     46.17 5843.2 1698.8
## - lunch_type:writing_score                1     30.25 5827.3 1699.2
## + test_prep:writing_score                 1      8.14 5788.9 1699.3
## + test_prep:math_score                    1      6.87 5790.2 1699.4
## + gender:parent_marital_status            3     45.91 5751.1 1699.5
## + parent_educ:is_first_child              5     84.41 5712.6 1699.5
## + transport_means:wkly_study_hours        2     25.60 5771.4 1699.5
## + transport_means:math_score              1      3.73 5793.3 1699.8
## - lunch_type:wkly_study_hours             2     56.40 5853.4 1699.8
## + gender:transport_means                  1      2.12 5794.9 1699.9
## + lunch_type:is_first_child               1      1.60 5795.4 1700.0
## + lunch_type:transport_means              1      1.14 5795.9 1700.0
## - test_prep:parent_marital_status         2     58.17 5855.2 1700.0
## + gender:test_prep                        1      1.03 5796.0 1700.0
## - is_first_child:transport_means          1     39.00 5836.0 1700.1
## + is_first_child:math_score               1      0.00 5797.0 1700.1
## - practice_sport:writing_score            2     59.43 5856.5 1700.2
## - gender:writing_score                    1     42.16 5839.2 1700.4
## + ethnic_group:test_prep                  4     55.64 5741.4 1700.5
## - gender:math_score                       1     42.87 5839.9 1700.5
## - ethnic_group:transport_means            4    103.53 5900.6 1700.6
## - parent_educ:test_prep                   5    123.58 5920.6 1700.6
## + is_first_child:wkly_study_hours         2     14.62 5782.4 1700.7
## - gender:parent_educ                      5    125.85 5922.9 1700.8
## - gender:practice_sport                   2     67.78 5864.8 1701.0
## - parent_marital_status:is_first_child    2     68.32 5865.4 1701.0
## - lunch_type:parent_marital_status        3     88.99 5886.0 1701.1
## - wkly_study_hours:math_score             2     70.85 5867.9 1701.3
## + practice_sport:transport_means          2      8.16 5788.9 1701.3
## + parent_marital_status:transport_means   3     24.28 5772.8 1701.7
## + practice_sport:wkly_study_hours         4     41.66 5755.4 1701.9
## - parent_marital_status:writing_score     3     97.04 5894.1 1701.9
## - parent_educ:math_score                  5    138.24 5935.3 1702.0
## + parent_educ:transport_means             5     58.99 5738.0 1702.1
## - test_prep:is_first_child                1     61.40 5858.4 1702.3
## + parent_marital_status:math_score        3     17.36 5779.7 1702.4
## - gender:wkly_study_hours                 2     81.91 5878.9 1702.4
## - ethnic_group:wkly_study_hours           8    205.57 6002.6 1702.7
## - wkly_study_hours:writing_score          2     85.84 5882.9 1702.8
## + parent_marital_status:practice_sport    4     32.32 5764.7 1702.8
## + parent_educ:writing_score               5     43.92 5753.1 1703.7
## - parent_educ:practice_sport             10    257.67 6054.7 1703.8
## - practice_sport:math_score               2     95.86 5892.9 1703.8
## - transport_means:writing_score           1     80.24 5877.3 1704.2
## - parent_educ:parent_marital_status      14    345.06 6142.1 1704.2
## + ethnic_group:is_first_child             4     18.37 5778.7 1704.3
## + ethnic_group:math_score                 4      2.96 5794.1 1705.8
## + gender:ethnic_group                     4      1.99 5795.0 1705.9
## + parent_educ:lunch_type                  5     18.66 5778.4 1706.2
## + parent_educ:wkly_study_hours           10    108.48 5688.6 1707.0
## - parent_marital_status:wkly_study_hours  5    224.56 6021.6 1710.6
## - ethnic_group:writing_score              4    212.86 6009.9 1711.4
## - ethnic_group:parent_educ               20    548.79 6345.8 1711.5
## - ethnic_group:lunch_type                 4    215.91 6012.9 1711.7
## - ethnic_group:parent_marital_status     10    454.57 6251.6 1722.7
## 
## Step:  AIC=1696.5
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:practice_sport               2     32.13 5852.4 1695.8
## - lunch_type:math_score                   1     13.63 5833.9 1695.9
## - gender:is_first_child                   1     15.91 5836.2 1696.1
## - is_first_child:writing_score            1     16.39 5836.7 1696.2
## - test_prep:transport_means               1     16.50 5836.8 1696.2
## - gender:lunch_type                       1     17.25 5837.5 1696.2
## - writing_score:math_score                1     17.67 5837.9 1696.3
## <none>                                                5820.3 1696.5
## - lunch_type:test_prep                    1     20.30 5840.6 1696.5
## - test_prep:practice_sport                2     43.98 5864.2 1696.9
## - practice_sport:is_first_child           2     45.32 5865.6 1697.1
## - lunch_type:writing_score                1     32.24 5852.5 1697.8
## + test_prep:writing_score                 1      5.63 5814.6 1697.9
## + test_prep:math_score                    1      4.06 5816.2 1698.1
## + test_prep:wkly_study_hours              2     23.24 5797.0 1698.1
## - ethnic_group:practice_sport             8    177.07 5997.3 1698.2
## + transport_means:math_score              1      3.01 5817.3 1698.2
## + transport_means:wkly_study_hours        2     22.59 5797.7 1698.2
## + parent_educ:is_first_child              5     80.40 5739.9 1698.3
## + gender:transport_means                  1      1.67 5818.6 1698.3
## + gender:parent_marital_status            3     40.92 5779.4 1698.3
## - wkly_study_hours:math_score             2     58.43 5878.7 1698.4
## + gender:test_prep                        1      0.91 5819.4 1698.4
## + lunch_type:is_first_child               1      0.44 5819.8 1698.5
## + lunch_type:transport_means              1      0.42 5819.9 1698.5
## + is_first_child:math_score               1      0.34 5819.9 1698.5
## - practice_sport:writing_score            2     59.32 5879.6 1698.5
## - gender:parent_educ                      5    119.63 5939.9 1698.5
## - lunch_type:wkly_study_hours             2     59.64 5879.9 1698.5
## - gender:writing_score                    1     41.77 5862.0 1698.7
## - is_first_child:transport_means          1     41.94 5862.2 1698.7
## - parent_educ:test_prep                   5    122.04 5942.3 1698.7
## - gender:math_score                       1     43.29 5863.6 1698.9
## - parent_marital_status:is_first_child    2     64.43 5884.7 1699.0
## - test_prep:parent_marital_status         2     66.39 5886.7 1699.2
## - gender:practice_sport                   2     67.26 5887.5 1699.3
## + is_first_child:wkly_study_hours         2     10.65 5809.6 1699.4
## - ethnic_group:transport_means            4    108.74 5929.0 1699.4
## + ethnic_group:test_prep                  4     49.62 5770.7 1699.5
## - lunch_type:parent_marital_status        3     90.26 5910.5 1699.6
## + practice_sport:transport_means          2      8.04 5812.2 1699.7
## - wkly_study_hours:writing_score          2     73.78 5894.1 1699.9
## + parent_marital_status:transport_means   3     25.26 5795.0 1699.9
## + practice_sport:wkly_study_hours         4     42.66 5777.6 1700.2
## - gender:wkly_study_hours                 2     76.66 5896.9 1700.2
## - parent_marital_status:writing_score     3     96.88 5917.2 1700.2
## + parent_educ:transport_means             5     60.08 5760.2 1700.4
## - test_prep:is_first_child                1     61.41 5881.7 1700.7
## + parent_marital_status:practice_sport    4     36.20 5784.1 1700.8
## + parent_marital_status:math_score        3     13.35 5806.9 1701.1
## - parent_educ:math_score                  5    146.86 5967.1 1701.2
## - ethnic_group:wkly_study_hours           8    211.83 6032.1 1701.6
## + parent_educ:writing_score               5     43.52 5776.8 1702.1
## - practice_sport:math_score               2     96.57 5916.8 1702.2
## - parent_educ:practice_sport             10    261.93 6082.2 1702.5
## - parent_educ:parent_marital_status      14    346.60 6166.9 1702.6
## + ethnic_group:is_first_child             4     14.92 5805.4 1703.0
## - transport_means:writing_score           1     87.51 5907.8 1703.3
## + ethnic_group:math_score                 4      3.24 5817.0 1704.2
## + gender:ethnic_group                     4      2.93 5817.3 1704.2
## + parent_educ:lunch_type                  5     19.29 5801.0 1704.5
## + parent_educ:wkly_study_hours           10    108.15 5712.1 1705.4
## - parent_marital_status:wkly_study_hours  5    225.81 6046.1 1709.0
## - ethnic_group:lunch_type                 4    205.74 6026.0 1709.0
## - ethnic_group:writing_score              4    211.28 6031.6 1709.5
## - ethnic_group:parent_educ               20    565.38 6385.7 1711.2
## - ethnic_group:parent_marital_status     10    466.66 6286.9 1722.0
## 
## Step:  AIC=1695.75
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:wkly_study_hours + 
##     lunch_type:writing_score + lunch_type:math_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:math_score                   1     10.89 5863.3 1694.8
## - gender:is_first_child                   1     13.47 5865.9 1695.1
## - gender:lunch_type                       1     14.22 5866.6 1695.2
## - test_prep:transport_means               1     14.77 5867.2 1695.2
## - is_first_child:writing_score            1     16.11 5868.5 1695.4
## - writing_score:math_score                1     17.08 5869.5 1695.5
## <none>                                                5852.4 1695.8
## - test_prep:practice_sport                2     40.04 5892.4 1695.8
## - lunch_type:test_prep                    1     22.00 5874.4 1696.0
## - practice_sport:is_first_child           2     44.68 5897.1 1696.2
## + lunch_type:practice_sport               2     32.13 5820.3 1696.5
## - lunch_type:writing_score                1     28.08 5880.5 1696.6
## - gender:writing_score                    1     34.35 5886.8 1697.2
## + test_prep:wkly_study_hours              2     24.95 5827.5 1697.2
## + test_prep:writing_score                 1      4.85 5847.6 1697.3
## - gender:math_score                       1     35.40 5887.8 1697.3
## + test_prep:math_score                    1      3.69 5848.7 1697.4
## + transport_means:math_score              1      3.69 5848.7 1697.4
## - wkly_study_hours:math_score             2     57.91 5910.3 1697.6
## + gender:transport_means                  1      1.85 5850.6 1697.6
## + gender:test_prep                        1      1.16 5851.2 1697.6
## + is_first_child:math_score               1      0.67 5851.7 1697.7
## + lunch_type:is_first_child               1      0.09 5852.3 1697.7
## + lunch_type:transport_means              1      0.08 5852.3 1697.7
## + transport_means:wkly_study_hours        2     19.59 5832.8 1697.8
## - lunch_type:wkly_study_hours             2     61.01 5913.4 1697.9
## - gender:parent_educ                      5    121.71 5974.1 1697.9
## + gender:parent_marital_status            3     37.02 5815.4 1698.0
## - test_prep:parent_marital_status         2     62.69 5915.1 1698.0
## + is_first_child:wkly_study_hours         2     15.42 5837.0 1698.2
## + parent_educ:is_first_child              5     74.18 5778.2 1698.2
## - practice_sport:writing_score            2     64.73 5917.1 1698.2
## - parent_marital_status:is_first_child    2     65.24 5917.6 1698.3
## + ethnic_group:test_prep                  4     50.54 5801.9 1698.6
## - lunch_type:parent_marital_status        3     89.05 5941.5 1698.7
## - gender:practice_sport                   2     69.40 5921.8 1698.7
## - is_first_child:transport_means          1     50.70 5903.1 1698.8
## - ethnic_group:transport_means            4    111.10 5963.5 1698.8
## + practice_sport:transport_means          2      8.66 5843.7 1698.9
## - wkly_study_hours:writing_score          2     72.56 5925.0 1699.0
## + parent_educ:transport_means             5     66.34 5786.1 1699.0
## - parent_marital_status:writing_score     3     94.90 5947.3 1699.2
## + parent_marital_status:transport_means   3     23.44 5829.0 1699.4
## - parent_educ:test_prep                   5    137.38 5989.8 1699.4
## - ethnic_group:practice_sport             8    199.43 6051.8 1699.5
## + parent_marital_status:practice_sport    4     38.57 5813.8 1699.8
## - test_prep:is_first_child                1     61.11 5913.5 1699.9
## + practice_sport:wkly_study_hours         4     37.71 5814.7 1699.9
## - gender:wkly_study_hours                 2     82.06 5934.5 1700.0
## - ethnic_group:wkly_study_hours           8    208.02 6060.4 1700.3
## - parent_educ:math_score                  5    147.20 5999.6 1700.4
## + parent_marital_status:math_score        3     12.05 5840.3 1700.5
## + parent_educ:writing_score               5     45.09 5807.3 1701.2
## - practice_sport:math_score               2    100.45 5952.8 1701.8
## + ethnic_group:is_first_child             4     15.73 5836.7 1702.2
## - transport_means:writing_score           1     85.85 5938.2 1702.3
## - parent_educ:parent_marital_status      14    360.09 6212.5 1703.0
## + gender:ethnic_group                     4      4.20 5848.2 1703.3
## + ethnic_group:math_score                 4      2.94 5849.5 1703.5
## - parent_educ:practice_sport             10    283.48 6135.9 1703.7
## + parent_educ:lunch_type                  5     20.52 5831.9 1703.7
## + parent_educ:wkly_study_hours           10    112.06 5740.3 1704.3
## - ethnic_group:lunch_type                 4    198.79 6051.2 1707.5
## - parent_marital_status:wkly_study_hours  5    226.28 6078.7 1708.1
## - ethnic_group:writing_score              4    214.10 6066.5 1709.0
## - ethnic_group:parent_educ               20    573.66 6426.1 1710.9
## - ethnic_group:parent_marital_status     10    470.73 6323.1 1721.4
## 
## Step:  AIC=1694.84
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:lunch_type + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + gender:writing_score + 
##     gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:wkly_study_hours + 
##     lunch_type:writing_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:lunch_type                       1      3.91 5867.2 1693.2
## - gender:is_first_child                   1     11.31 5874.6 1694.0
## - test_prep:transport_means               1     13.99 5877.3 1694.2
## - is_first_child:writing_score            1     14.42 5877.7 1694.3
## - lunch_type:test_prep                    1     15.73 5879.0 1694.4
## - test_prep:practice_sport                2     37.88 5901.2 1694.6
## <none>                                                5863.3 1694.8
## - writing_score:math_score                1     24.14 5887.4 1695.3
## - practice_sport:is_first_child           2     44.92 5908.2 1695.3
## - lunch_type:writing_score                1     25.39 5888.7 1695.4
## + lunch_type:math_score                   1     10.89 5852.4 1695.8
## + lunch_type:practice_sport               2     29.38 5833.9 1695.9
## - gender:writing_score                    1     33.76 5897.0 1696.2
## + test_prep:writing_score                 1      5.42 5857.9 1696.3
## + test_prep:wkly_study_hours              2     24.75 5838.5 1696.3
## - gender:math_score                       1     34.97 5898.3 1696.3
## + test_prep:math_score                    1      4.36 5858.9 1696.4
## - wkly_study_hours:math_score             2     55.66 5918.9 1696.4
## + transport_means:math_score              1      4.06 5859.2 1696.4
## - gender:parent_educ                      5    117.77 5981.1 1696.6
## + transport_means:wkly_study_hours        2     21.71 5841.6 1696.7
## + gender:transport_means                  1      1.82 5861.5 1696.7
## + gender:test_prep                        1      1.55 5861.7 1696.7
## + lunch_type:transport_means              1      0.34 5862.9 1696.8
## + is_first_child:math_score               1      0.33 5863.0 1696.8
## + lunch_type:is_first_child               1      0.04 5863.3 1696.8
## - lunch_type:wkly_study_hours             2     62.36 5925.6 1697.1
## - parent_marital_status:is_first_child    2     62.37 5925.7 1697.1
## - lunch_type:parent_marital_status        3     83.61 5946.9 1697.2
## - test_prep:parent_marital_status         2     63.55 5926.8 1697.2
## + parent_educ:is_first_child              5     74.96 5788.3 1697.2
## + is_first_child:wkly_study_hours         2     15.64 5847.7 1697.3
## + gender:parent_marital_status            3     35.13 5828.2 1697.3
## - practice_sport:writing_score            2     66.22 5929.5 1697.5
## - ethnic_group:transport_means            4    107.86 5971.1 1697.6
## - gender:practice_sport                   2     68.26 5931.5 1697.7
## - parent_marital_status:writing_score     3     89.03 5952.3 1697.7
## - wkly_study_hours:writing_score          2     69.70 5933.0 1697.8
## + practice_sport:transport_means          2      8.75 5854.5 1698.0
## + ethnic_group:test_prep                  4     46.91 5816.4 1698.1
## - is_first_child:transport_means          1     54.77 5918.1 1698.3
## + parent_educ:transport_means             5     63.26 5800.0 1698.4
## - parent_educ:test_prep                   5    137.76 6001.1 1698.5
## + parent_marital_status:transport_means   3     20.74 5842.6 1698.8
## - gender:wkly_study_hours                 2     79.24 5942.5 1698.8
## + parent_marital_status:practice_sport    4     40.06 5823.2 1698.8
## - ethnic_group:practice_sport             8    201.81 6065.1 1698.8
## - test_prep:is_first_child                1     60.77 5924.1 1698.9
## + practice_sport:wkly_study_hours         4     37.86 5825.4 1699.0
## - ethnic_group:wkly_study_hours           8    208.79 6072.1 1699.5
## - parent_educ:math_score                  5    148.49 6011.8 1699.6
## + parent_marital_status:math_score        3     11.56 5851.7 1699.7
## + parent_educ:writing_score               5     43.34 5819.9 1700.5
## - practice_sport:math_score               2    101.61 5964.9 1701.0
## - transport_means:writing_score           1     84.70 5948.0 1701.3
## + ethnic_group:is_first_child             4     14.88 5848.4 1701.3
## - parent_educ:parent_marital_status      14    353.23 6216.5 1701.4
## + gender:ethnic_group                     4      4.60 5858.7 1702.4
## + ethnic_group:math_score                 4      2.73 5860.6 1702.6
## + parent_educ:lunch_type                  5     20.73 5842.6 1702.8
## - parent_educ:practice_sport             10    284.88 6148.2 1702.8
## + parent_educ:wkly_study_hours           10    108.79 5754.5 1703.8
## - ethnic_group:lunch_type                 4    188.67 6052.0 1705.5
## - parent_marital_status:wkly_study_hours  5    220.74 6084.0 1706.7
## - ethnic_group:writing_score              4    212.27 6075.6 1707.8
## - ethnic_group:parent_educ               20    572.96 6436.2 1709.8
## - ethnic_group:parent_marital_status     10    464.08 6327.4 1719.8
## 
## Step:  AIC=1693.24
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:practice_sport + gender:is_first_child + 
##     gender:wkly_study_hours + gender:writing_score + gender:math_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:wkly_study_hours + 
##     lunch_type:writing_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - gender:is_first_child                   1     11.12 5878.3 1692.3
## - test_prep:transport_means               1     13.28 5880.5 1692.6
## - lunch_type:test_prep                    1     13.98 5881.2 1692.6
## - is_first_child:writing_score            1     14.12 5881.3 1692.7
## - test_prep:practice_sport                2     36.93 5904.1 1692.9
## <none>                                                5867.2 1693.2
## - writing_score:math_score                1     21.18 5888.4 1693.4
## - lunch_type:writing_score                1     21.49 5888.7 1693.4
## - practice_sport:is_first_child           2     42.85 5910.1 1693.5
## + lunch_type:practice_sport               2     28.82 5838.4 1694.3
## - gender:math_score                       1     31.18 5898.4 1694.4
## - gender:writing_score                    1     31.30 5898.5 1694.4
## + test_prep:wkly_study_hours              2     25.36 5841.8 1694.7
## + test_prep:writing_score                 1      5.03 5862.2 1694.7
## + transport_means:math_score              1      4.44 5862.8 1694.8
## + test_prep:math_score                    1      3.98 5863.2 1694.8
## + gender:lunch_type                       1      3.91 5863.3 1694.8
## + gender:transport_means                  1      1.99 5865.2 1695.0
## - gender:parent_educ                      5    118.59 5985.8 1695.0
## + gender:test_prep                        1      1.85 5865.3 1695.0
## + transport_means:wkly_study_hours        2     21.17 5846.0 1695.1
## + lunch_type:math_score                   1      0.57 5866.6 1695.2
## + lunch_type:transport_means              1      0.43 5866.8 1695.2
## + is_first_child:math_score               1      0.28 5866.9 1695.2
## + lunch_type:is_first_child               1      0.00 5867.2 1695.2
## - wkly_study_hours:math_score             2     60.56 5927.8 1695.3
## - parent_marital_status:is_first_child    2     61.80 5929.0 1695.4
## - test_prep:parent_marital_status         2     62.34 5929.5 1695.5
## + parent_educ:is_first_child              5     76.68 5790.5 1695.5
## + gender:parent_marital_status            3     36.43 5830.8 1695.6
## - lunch_type:wkly_study_hours             2     63.76 5931.0 1695.6
## + is_first_child:wkly_study_hours         2     14.84 5852.4 1695.7
## - lunch_type:parent_marital_status        3     85.63 5952.8 1695.8
## - ethnic_group:transport_means            4    107.07 5974.3 1695.9
## - practice_sport:writing_score            2     68.41 5935.6 1696.1
## - gender:practice_sport                   2     68.63 5935.8 1696.1
## - parent_marital_status:writing_score     3     90.06 5957.3 1696.2
## + practice_sport:transport_means          2      8.69 5858.5 1696.4
## - wkly_study_hours:writing_score          2     73.28 5940.5 1696.6
## + ethnic_group:test_prep                  4     45.94 5821.3 1696.6
## - ethnic_group:practice_sport             8    199.26 6066.5 1696.9
## - parent_educ:test_prep                   5    138.12 6005.3 1697.0
## - is_first_child:transport_means          1     57.29 5924.5 1697.0
## + parent_marital_status:transport_means   3     21.29 5845.9 1697.1
## - test_prep:is_first_child                1     58.80 5926.0 1697.1
## - gender:wkly_study_hours                 2     79.39 5946.6 1697.2
## + parent_marital_status:practice_sport    4     40.10 5827.1 1697.2
## + parent_educ:transport_means             5     59.42 5807.8 1697.2
## + practice_sport:wkly_study_hours         4     38.24 5829.0 1697.4
## - ethnic_group:wkly_study_hours           8    206.65 6073.9 1697.7
## - parent_educ:math_score                  5    146.33 6013.5 1697.8
## + parent_marital_status:math_score        3     13.17 5854.0 1697.9
## + parent_educ:writing_score               5     41.70 5825.5 1699.0
## - transport_means:writing_score           1     83.51 5950.7 1699.6
## - practice_sport:math_score               2    103.74 5970.9 1699.6
## + ethnic_group:is_first_child             4     14.57 5852.6 1699.8
## - parent_educ:parent_marital_status      14    354.13 6221.3 1699.8
## + gender:ethnic_group                     4      4.52 5862.7 1700.8
## + ethnic_group:math_score                 4      2.87 5864.3 1701.0
## + parent_educ:lunch_type                  5     20.62 5846.6 1701.2
## - parent_educ:practice_sport             10    286.45 6153.6 1701.4
## + parent_educ:wkly_study_hours           10    109.22 5758.0 1702.2
## - ethnic_group:lunch_type                 4    190.93 6058.1 1704.1
## - parent_marital_status:wkly_study_hours  5    218.94 6086.1 1704.8
## - ethnic_group:writing_score              4    219.50 6086.7 1706.9
## - ethnic_group:parent_educ               20    569.20 6436.4 1707.9
## - ethnic_group:parent_marital_status     10    462.11 6329.3 1718.0
## 
## Step:  AIC=1692.35
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:practice_sport + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:wkly_study_hours + 
##     lunch_type:writing_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + is_first_child:writing_score + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - is_first_child:writing_score            1      8.43 5886.7 1691.2
## - lunch_type:test_prep                    1     12.58 5890.9 1691.6
## - test_prep:transport_means               1     13.56 5891.9 1691.7
## - test_prep:practice_sport                2     37.74 5916.1 1692.1
## <none>                                                5878.3 1692.3
## - lunch_type:writing_score                1     20.95 5899.3 1692.5
## - writing_score:math_score                1     21.44 5899.8 1692.5
## - practice_sport:is_first_child           2     43.80 5922.1 1692.7
## + gender:is_first_child                   1     11.12 5867.2 1693.2
## - gender:writing_score                    1     30.05 5908.4 1693.4
## - gender:math_score                       1     31.06 5909.4 1693.5
## + is_first_child:math_score               1      8.27 5870.1 1693.5
## + lunch_type:practice_sport               2     27.04 5851.3 1693.6
## + test_prep:writing_score                 1      6.34 5872.0 1693.7
## + test_prep:wkly_study_hours              2     25.56 5852.8 1693.8
## + transport_means:math_score              1      5.10 5873.2 1693.8
## + test_prep:math_score                    1      4.56 5873.8 1693.9
## + gender:lunch_type                       1      3.72 5874.6 1694.0
## - parent_marital_status:is_first_child    2     56.92 5935.2 1694.0
## + transport_means:wkly_study_hours        2     22.52 5855.8 1694.1
## - gender:parent_educ                      5    118.29 5996.6 1694.1
## + gender:test_prep                        1      2.29 5876.0 1694.1
## + parent_educ:is_first_child              5     81.35 5797.0 1694.1
## + gender:transport_means                  1      2.10 5876.2 1694.1
## + lunch_type:transport_means              1      0.79 5877.5 1694.3
## - wkly_study_hours:math_score             2     59.59 5937.9 1694.3
## + lunch_type:is_first_child               1      0.36 5878.0 1694.3
## + lunch_type:math_score                   1      0.33 5878.0 1694.3
## - test_prep:parent_marital_status         2     63.10 5941.4 1694.7
## - lunch_type:wkly_study_hours             2     64.38 5942.7 1694.8
## + gender:parent_marital_status            3     35.29 5843.0 1694.8
## - ethnic_group:transport_means            4    105.33 5983.7 1694.8
## - practice_sport:writing_score            2     65.75 5944.1 1694.9
## - lunch_type:parent_marital_status        3     86.19 5964.5 1694.9
## - gender:practice_sport                   2     66.13 5944.5 1695.0
## + is_first_child:wkly_study_hours         2     13.39 5864.9 1695.0
## - parent_marital_status:writing_score     3     89.81 5968.1 1695.3
## - wkly_study_hours:writing_score          2     71.99 5950.3 1695.5
## - test_prep:is_first_child                1     52.34 5930.7 1695.6
## + ethnic_group:test_prep                  4     46.82 5831.5 1695.6
## - ethnic_group:practice_sport             8    195.30 6073.6 1695.6
## + practice_sport:transport_means          2      7.06 5871.3 1695.6
## - parent_educ:test_prep                   5    134.57 6012.9 1695.7
## + parent_marital_status:transport_means   3     20.89 5857.4 1696.2
## + parent_marital_status:practice_sport    4     40.70 5837.6 1696.2
## - gender:wkly_study_hours                 2     79.30 5957.6 1696.3
## + parent_educ:transport_means             5     59.70 5818.6 1696.3
## - is_first_child:transport_means          1     60.02 5938.3 1696.3
## - ethnic_group:wkly_study_hours           8    203.40 6081.7 1696.4
## + practice_sport:wkly_study_hours         4     39.02 5839.3 1696.4
## + parent_marital_status:math_score        3     11.88 5866.4 1697.2
## - parent_educ:math_score                  5    152.54 6030.9 1697.5
## + parent_educ:writing_score               5     43.02 5835.3 1698.0
## - practice_sport:math_score               2    101.53 5979.8 1698.5
## - transport_means:writing_score           1     84.99 5963.3 1698.8
## - parent_educ:parent_marital_status      14    354.15 6232.5 1698.9
## + ethnic_group:is_first_child             4     13.19 5865.1 1699.0
## + gender:ethnic_group                     4      5.86 5872.5 1699.8
## + ethnic_group:math_score                 4      2.38 5875.9 1700.1
## + parent_educ:lunch_type                  5     20.69 5857.6 1700.3
## + parent_educ:wkly_study_hours           10    115.36 5763.0 1700.7
## - parent_educ:practice_sport             10    289.90 6168.2 1700.8
## - ethnic_group:lunch_type                 4    191.98 6070.3 1703.3
## - parent_marital_status:wkly_study_hours  5    217.55 6095.9 1703.8
## - ethnic_group:writing_score              4    219.33 6097.6 1706.0
## - ethnic_group:parent_educ               20    566.91 6445.2 1706.7
## - ethnic_group:parent_marital_status     10    466.20 6344.5 1717.4
## 
## Step:  AIC=1691.2
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:practice_sport + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep + 
##     lunch_type:parent_marital_status + lunch_type:wkly_study_hours + 
##     lunch_type:writing_score + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     parent_marital_status:writing_score + practice_sport:is_first_child + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + transport_means:writing_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score + 
##     writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:test_prep                    1     12.43 5899.2 1690.4
## - test_prep:transport_means               1     12.44 5899.2 1690.4
## - test_prep:practice_sport                2     39.61 5926.4 1691.2
## <none>                                                5886.7 1691.2
## - practice_sport:is_first_child           2     42.01 5928.8 1691.4
## - lunch_type:writing_score                1     22.57 5909.3 1691.5
## + is_first_child:math_score               1     16.22 5870.5 1691.6
## - writing_score:math_score                1     25.55 5912.3 1691.8
## - gender:writing_score                    1     28.30 5915.0 1692.0
## - gender:math_score                       1     29.44 5916.2 1692.1
## + parent_educ:is_first_child              5     88.77 5798.0 1692.2
## + is_first_child:writing_score            1      8.43 5878.3 1692.3
## - parent_marital_status:is_first_child    2     51.92 5938.7 1692.4
## + lunch_type:practice_sport               2     27.40 5859.3 1692.5
## + test_prep:writing_score                 1      6.10 5880.6 1692.6
## + test_prep:wkly_study_hours              2     25.61 5861.1 1692.6
## + gender:is_first_child                   1      5.42 5881.3 1692.7
## + test_prep:math_score                    1      5.41 5881.3 1692.7
## + transport_means:math_score              1      5.41 5881.3 1692.7
## + gender:lunch_type                       1      3.53 5883.2 1692.8
## - gender:parent_educ                      5    117.57 6004.3 1692.9
## + gender:transport_means                  1      2.78 5884.0 1692.9
## + transport_means:wkly_study_hours        2     22.50 5864.2 1692.9
## + lunch_type:is_first_child               1      1.98 5884.8 1693.0
## + gender:test_prep                        1      1.19 5885.6 1693.1
## - wkly_study_hours:math_score             2     59.06 5945.8 1693.1
## + lunch_type:transport_means              1      1.02 5885.7 1693.1
## + lunch_type:math_score                   1      0.28 5886.5 1693.2
## - test_prep:parent_marital_status         2     61.18 5947.9 1693.3
## - ethnic_group:transport_means            4    103.66 5990.4 1693.5
## + gender:parent_marital_status            3     35.77 5851.0 1693.6
## - lunch_type:wkly_study_hours             2     64.37 5951.1 1693.6
## - gender:practice_sport                   2     64.76 5951.5 1693.7
## - parent_marital_status:writing_score     3     85.46 5972.2 1693.7
## - test_prep:is_first_child                1     45.80 5932.5 1693.8
## - lunch_type:parent_marital_status        3     86.41 5973.2 1693.8
## - practice_sport:writing_score            2     66.46 5953.2 1693.8
## + is_first_child:wkly_study_hours         2     12.15 5874.6 1694.0
## - ethnic_group:practice_sport             8    190.92 6077.7 1694.0
## - wkly_study_hours:writing_score          2     69.90 5956.6 1694.2
## + ethnic_group:test_prep                  4     48.66 5838.1 1694.3
## + practice_sport:transport_means          2      7.87 5878.9 1694.4
## - parent_educ:test_prep                   5    133.98 6020.7 1694.5
## - gender:wkly_study_hours                 2     77.47 5964.2 1694.9
## + parent_marital_status:transport_means   3     22.08 5864.7 1695.0
## + parent_marital_status:practice_sport    4     41.77 5845.0 1695.0
## - ethnic_group:wkly_study_hours           8    201.56 6088.3 1695.1
## - is_first_child:transport_means          1     59.23 5946.0 1695.1
## + practice_sport:wkly_study_hours         4     40.45 5846.3 1695.1
## + parent_educ:transport_means             5     58.77 5828.0 1695.3
## - parent_educ:math_score                  5    147.79 6034.5 1695.8
## + parent_marital_status:math_score        3     11.83 5874.9 1696.0
## + parent_educ:writing_score               5     45.41 5841.3 1696.6
## - parent_educ:parent_marital_status      14    347.41 6234.2 1697.0
## - transport_means:writing_score           1     81.02 5967.8 1697.3
## - practice_sport:math_score               2    102.76 5989.5 1697.4
## + ethnic_group:is_first_child             4     10.04 5876.7 1698.2
## + gender:ethnic_group                     4      5.97 5880.8 1698.6
## + ethnic_group:math_score                 4      1.90 5884.8 1699.0
## + parent_educ:lunch_type                  5     19.46 5867.3 1699.2
## - parent_educ:practice_sport             10    290.44 6177.2 1699.6
## + parent_educ:wkly_study_hours           10    114.38 5772.4 1699.6
## - ethnic_group:lunch_type                 4    189.41 6076.2 1701.9
## - parent_marital_status:wkly_study_hours  5    214.11 6100.9 1702.3
## - ethnic_group:writing_score              4    215.39 6102.1 1704.4
## - ethnic_group:parent_educ               20    561.52 6448.3 1705.0
## - ethnic_group:parent_marital_status     10    463.57 6350.3 1715.9
## 
## Step:  AIC=1690.44
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:practice_sport + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:transport_means               1     12.25 5911.4 1689.7
## - lunch_type:writing_score                1     15.93 5915.1 1690.0
## - test_prep:practice_sport                2     37.78 5937.0 1690.2
## <none>                                                5899.2 1690.4
## - practice_sport:is_first_child           2     42.62 5941.8 1690.7
## + is_first_child:math_score               1     15.92 5883.3 1690.8
## - writing_score:math_score                1     24.73 5923.9 1690.9
## - gender:writing_score                    1     27.35 5926.5 1691.2
## + lunch_type:test_prep                    1     12.43 5886.7 1691.2
## + parent_educ:is_first_child              5     89.27 5809.9 1691.5
## - gender:math_score                       1     30.28 5929.5 1691.5
## + lunch_type:practice_sport               2     29.56 5869.6 1691.5
## + test_prep:wkly_study_hours              2     29.14 5870.0 1691.5
## + is_first_child:writing_score            1      8.28 5890.9 1691.6
## - parent_marital_status:is_first_child    2     51.96 5951.1 1691.6
## + transport_means:math_score              1      5.83 5893.3 1691.9
## + gender:is_first_child                   1      4.54 5894.6 1692.0
## + lunch_type:is_first_child               1      2.50 5896.7 1692.2
## + gender:transport_means                  1      2.48 5896.7 1692.2
## - gender:parent_educ                      5    118.69 6017.9 1692.2
## - wkly_study_hours:math_score             2     58.06 5957.2 1692.2
## + gender:lunch_type                       1      1.97 5897.2 1692.2
## + lunch_type:transport_means              1      1.92 5897.3 1692.2
## + test_prep:writing_score                 1      1.71 5897.5 1692.3
## + gender:test_prep                        1      1.50 5897.7 1692.3
## + test_prep:math_score                    1      0.58 5898.6 1692.4
## + lunch_type:math_score                   1      0.06 5899.1 1692.4
## + gender:parent_marital_status            3     39.32 5859.9 1692.5
## + transport_means:wkly_study_hours        2     19.04 5880.1 1692.5
## - ethnic_group:transport_means            4    103.75 6002.9 1692.7
## - test_prep:parent_marital_status         2     65.17 5964.3 1692.9
## - test_prep:is_first_child                1     45.35 5944.5 1693.0
## - lunch_type:wkly_study_hours             2     66.00 5965.2 1693.0
## - ethnic_group:practice_sport             8    189.85 6089.0 1693.1
## - wkly_study_hours:writing_score          2     69.72 5968.9 1693.4
## - practice_sport:writing_score            2     69.75 5968.9 1693.4
## + is_first_child:wkly_study_hours         2     10.58 5888.6 1693.4
## - parent_marital_status:writing_score     3     90.40 5989.6 1693.4
## + practice_sport:transport_means          2      9.55 5889.6 1693.5
## - lunch_type:parent_marital_status        3     91.23 5990.4 1693.5
## + ethnic_group:test_prep                  4     49.00 5850.2 1693.5
## - gender:practice_sport                   2     71.32 5970.5 1693.5
## - is_first_child:transport_means          1     55.64 5954.8 1694.0
## - gender:wkly_study_hours                 2     77.53 5976.7 1694.2
## + parent_marital_status:practice_sport    4     42.71 5856.5 1694.2
## + parent_marital_status:transport_means   3     22.10 5877.1 1694.2
## - parent_educ:test_prep                   5    141.35 6040.5 1694.4
## + parent_educ:transport_means             5     58.31 5840.9 1694.6
## + practice_sport:wkly_study_hours         4     34.72 5864.5 1695.0
## + parent_marital_status:math_score        3     14.14 5885.0 1695.0
## - parent_educ:math_score                  5    150.70 6049.9 1695.3
## - parent_educ:parent_marital_status      14    339.49 6238.7 1695.5
## - ethnic_group:wkly_study_hours           8    214.12 6113.3 1695.5
## + parent_educ:writing_score               5     46.77 5852.4 1695.8
## - transport_means:writing_score           1     83.01 5982.2 1696.7
## - practice_sport:math_score               2    106.94 6006.1 1697.0
## + ethnic_group:is_first_child             4     11.60 5887.6 1697.3
## + gender:ethnic_group                     4      5.72 5893.5 1697.9
## + parent_educ:lunch_type                  5     22.71 5876.5 1698.2
## + ethnic_group:math_score                 4      2.06 5897.1 1698.2
## - parent_educ:practice_sport             10    288.27 6187.4 1698.6
## + parent_educ:wkly_study_hours           10    109.01 5790.2 1699.4
## - ethnic_group:lunch_type                 4    182.54 6081.7 1700.4
## - parent_marital_status:wkly_study_hours  5    207.87 6107.0 1700.9
## - ethnic_group:writing_score              4    212.67 6111.8 1703.3
## - ethnic_group:parent_educ               20    560.24 6459.4 1704.0
## - ethnic_group:parent_marital_status     10    484.31 6383.5 1717.0
## 
## Step:  AIC=1689.67
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:practice_sport + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status + 
##     lunch_type:wkly_study_hours + lunch_type:writing_score + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - lunch_type:writing_score                1     15.55 5927.0 1689.2
## - test_prep:practice_sport                2     37.89 5949.3 1689.4
## <none>                                                5911.4 1689.7
## - practice_sport:is_first_child           2     42.53 5954.0 1689.9
## - writing_score:math_score                1     24.01 5935.4 1690.1
## - gender:writing_score                    1     25.56 5937.0 1690.2
## + is_first_child:math_score               1     14.41 5897.0 1690.2
## + test_prep:transport_means               1     12.25 5899.2 1690.4
## + lunch_type:test_prep                    1     12.24 5899.2 1690.4
## - gender:math_score                       1     30.06 5941.5 1690.7
## + test_prep:wkly_study_hours              2     29.98 5881.4 1690.7
## - parent_marital_status:is_first_child    2     51.50 5962.9 1690.8
## + lunch_type:practice_sport               2     28.06 5883.4 1690.9
## + parent_educ:is_first_child              5     86.91 5824.5 1690.9
## + transport_means:math_score              1      7.35 5904.1 1690.9
## + is_first_child:writing_score            1      7.18 5904.2 1691.0
## - ethnic_group:transport_means            4     95.91 6007.3 1691.2
## + gender:is_first_child                   1      4.96 5906.5 1691.2
## + lunch_type:transport_means              1      3.41 5908.0 1691.3
## + lunch_type:is_first_child               1      1.70 5909.7 1691.5
## + gender:lunch_type                       1      1.51 5909.9 1691.5
## + test_prep:writing_score                 1      1.29 5910.1 1691.5
## - wkly_study_hours:math_score             2     59.29 5970.7 1691.5
## + gender:test_prep                        1      0.95 5910.5 1691.6
## + gender:transport_means                  1      0.86 5910.6 1691.6
## + test_prep:math_score                    1      0.39 5911.0 1691.6
## + lunch_type:math_score                   1      0.09 5911.3 1691.7
## - test_prep:parent_marital_status         2     60.68 5972.1 1691.7
## + gender:parent_marital_status            3     39.33 5872.1 1691.7
## + transport_means:wkly_study_hours        2     18.95 5892.5 1691.8
## - gender:parent_educ                      5    124.02 6035.4 1691.9
## - test_prep:is_first_child                1     43.58 5955.0 1692.0
## - ethnic_group:practice_sport             8    189.86 6101.3 1692.3
## + ethnic_group:test_prep                  4     53.26 5858.2 1692.3
## - practice_sport:writing_score            2     67.87 5979.3 1692.4
## - parent_marital_status:writing_score     3     88.30 5999.7 1692.4
## - gender:practice_sport                   2     68.65 5980.1 1692.5
## - lunch_type:parent_marital_status        3     89.57 6001.0 1692.5
## + is_first_child:wkly_study_hours         2     10.41 5901.0 1692.6
## - wkly_study_hours:writing_score          2     72.31 5983.7 1692.8
## + practice_sport:transport_means          2      7.75 5903.7 1692.9
## - lunch_type:wkly_study_hours             2     73.89 5985.3 1693.0
## + parent_marital_status:practice_sport    4     43.58 5867.8 1693.3
## - gender:wkly_study_hours                 2     78.42 5989.8 1693.4
## - is_first_child:transport_means          1     58.71 5970.1 1693.5
## - parent_educ:test_prep                   5    143.50 6054.9 1693.8
## + parent_marital_status:transport_means   3     18.25 5893.2 1693.8
## - ethnic_group:wkly_study_hours           8    207.30 6118.7 1694.0
## + parent_educ:transport_means             5     56.18 5855.2 1694.0
## + parent_marital_status:math_score        3     15.33 5896.1 1694.1
## + practice_sport:wkly_study_hours         4     32.20 5879.2 1694.4
## - parent_educ:parent_marital_status      14    338.06 6249.5 1694.5
## - parent_educ:math_score                  5    152.83 6064.3 1694.7
## - transport_means:writing_score           1     71.87 5983.3 1694.8
## + parent_educ:writing_score               5     44.22 5867.2 1695.2
## - practice_sport:math_score               2    105.16 6016.6 1696.1
## + ethnic_group:is_first_child             4     12.91 5898.5 1696.4
## + gender:ethnic_group                     4      5.97 5905.5 1697.1
## - parent_educ:practice_sport             10    281.22 6192.6 1697.1
## + parent_educ:lunch_type                  5     24.49 5886.9 1697.2
## + ethnic_group:math_score                 4      1.82 5909.6 1697.5
## + parent_educ:wkly_study_hours           10    112.19 5799.2 1698.4
## - ethnic_group:lunch_type                 4    176.49 6087.9 1699.0
## - parent_marital_status:wkly_study_hours  5    209.71 6121.1 1700.2
## - ethnic_group:writing_score              4    206.40 6117.8 1701.9
## - ethnic_group:parent_educ               20    550.34 6461.8 1702.2
## - ethnic_group:parent_marital_status     10    489.04 6400.5 1716.6
## 
## Step:  AIC=1689.22
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:practice_sport + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score + writing_score:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - writing_score:math_score                1     11.36 5938.3 1688.3
## - test_prep:practice_sport                2     36.79 5963.8 1688.9
## <none>                                                5927.0 1689.2
## - practice_sport:is_first_child           2     42.54 5969.5 1689.4
## + lunch_type:writing_score                1     15.55 5911.4 1689.7
## + is_first_child:math_score               1     15.07 5911.9 1689.7
## + test_prep:wkly_study_hours              2     32.14 5894.8 1690.0
## - gender:writing_score                    1     28.29 5955.3 1690.0
## + test_prep:transport_means               1     11.87 5915.1 1690.0
## + is_first_child:writing_score            1      8.52 5918.5 1690.4
## + lunch_type:practice_sport               2     27.32 5899.7 1690.5
## + transport_means:math_score              1      7.03 5919.9 1690.5
## + lunch_type:math_score                   1      6.95 5920.0 1690.5
## + parent_educ:is_first_child              5     86.50 5840.5 1690.5
## + lunch_type:test_prep                    1      5.72 5921.3 1690.7
## - gender:math_score                       1     34.80 5961.8 1690.7
## + gender:is_first_child                   1      4.59 5922.4 1690.8
## - parent_marital_status:is_first_child    2     56.16 5983.1 1690.8
## + lunch_type:transport_means              1      3.48 5923.5 1690.9
## - gender:parent_educ                      5    119.47 6046.5 1691.0
## + lunch_type:is_first_child               1      1.41 5925.6 1691.1
## + gender:transport_means                  1      0.76 5926.2 1691.1
## + gender:test_prep                        1      0.73 5926.3 1691.1
## + transport_means:wkly_study_hours        2     20.66 5906.3 1691.2
## + test_prep:writing_score                 1      0.36 5926.6 1691.2
## + gender:lunch_type                       1      0.19 5926.8 1691.2
## + test_prep:math_score                    1      0.06 5926.9 1691.2
## + gender:parent_marital_status            3     39.57 5887.4 1691.3
## + ethnic_group:test_prep                  4     58.10 5868.9 1691.4
## - ethnic_group:transport_means            4    103.61 6030.6 1691.4
## - test_prep:parent_marital_status         2     63.41 5990.4 1691.5
## - test_prep:is_first_child                1     43.27 5970.2 1691.5
## - wkly_study_hours:math_score             2     65.79 5992.8 1691.7
## + is_first_child:wkly_study_hours         2     10.49 5916.5 1692.2
## - gender:practice_sport                   2     71.09 5998.1 1692.2
## - practice_sport:writing_score            2     71.50 5998.5 1692.3
## - ethnic_group:practice_sport             8    195.15 6122.1 1692.3
## + parent_marital_status:practice_sport    4     48.88 5878.1 1692.3
## - lunch_type:parent_marital_status        3     93.82 6020.8 1692.5
## + practice_sport:transport_means          2      7.16 5919.8 1692.5
## - wkly_study_hours:writing_score          2     74.64 6001.6 1692.6
## - ethnic_group:wkly_study_hours           8    200.15 6127.1 1692.8
## - lunch_type:wkly_study_hours             2     78.06 6005.0 1692.9
## - gender:wkly_study_hours                 2     79.96 6006.9 1693.1
## - parent_educ:test_prep                   5    142.47 6069.5 1693.2
## - parent_marital_status:writing_score     3    101.61 6028.6 1693.2
## + parent_marital_status:transport_means   3     19.41 5907.6 1693.3
## - is_first_child:transport_means          1     62.87 5989.8 1693.4
## + parent_marital_status:math_score        3     16.76 5910.2 1693.5
## + parent_educ:transport_means             5     54.19 5872.8 1693.8
## + practice_sport:wkly_study_hours         4     33.36 5893.6 1693.9
## - parent_educ:parent_marital_status      14    340.95 6267.9 1694.2
## - parent_educ:math_score                  5    153.92 6080.9 1694.3
## - transport_means:writing_score           1     73.63 6000.6 1694.5
## + parent_educ:writing_score               5     37.49 5889.5 1695.5
## - practice_sport:math_score               2    108.51 6035.5 1695.9
## + ethnic_group:is_first_child             4     12.94 5914.0 1695.9
## + parent_educ:lunch_type                  5     26.51 5900.5 1696.6
## - parent_educ:practice_sport             10    281.57 6208.5 1696.6
## + gender:ethnic_group                     4      5.15 5921.8 1696.7
## + ethnic_group:math_score                 4      2.74 5924.2 1696.9
## - ethnic_group:lunch_type                 4    171.72 6098.7 1698.1
## + parent_educ:wkly_study_hours           10    105.62 5821.4 1698.6
## - parent_marital_status:wkly_study_hours  5    214.43 6141.4 1700.2
## - ethnic_group:parent_educ               20    542.46 6469.4 1700.9
## - ethnic_group:writing_score              4    212.08 6139.1 1702.0
## - ethnic_group:parent_marital_status     10    480.12 6407.1 1715.2
## 
## Step:  AIC=1688.35
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:practice_sport + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - test_prep:practice_sport                2     34.25 5972.6 1687.7
## <none>                                                5938.3 1688.3
## - practice_sport:is_first_child           2     42.31 5980.6 1688.5
## + is_first_child:math_score               1     18.12 5920.2 1688.5
## - gender:writing_score                    1     24.36 5962.7 1688.8
## + test_prep:wkly_study_hours              2     32.33 5906.0 1689.1
## + test_prep:transport_means               1     11.48 5926.9 1689.2
## + writing_score:math_score                1     11.36 5927.0 1689.2
## + is_first_child:writing_score            1     10.84 5927.5 1689.3
## - gender:math_score                       1     30.76 5969.1 1689.4
## + lunch_type:test_prep                    1      7.73 5930.6 1689.6
## + lunch_type:practice_sport               2     26.76 5911.6 1689.7
## - parent_marital_status:is_first_child    2     54.56 5992.9 1689.7
## + transport_means:math_score              1      5.96 5932.4 1689.8
## + gender:is_first_child                   1      4.27 5934.1 1689.9
## + gender:parent_marital_status            3     43.73 5894.6 1690.0
## + parent_educ:is_first_child              5     83.40 5854.9 1690.0
## + lunch_type:transport_means              1      3.17 5935.2 1690.0
## + lunch_type:writing_score                1      2.91 5935.4 1690.1
## + lunch_type:is_first_child               1      1.34 5937.0 1690.2
## + test_prep:math_score                    1      0.92 5937.4 1690.3
## + gender:test_prep                        1      0.91 5937.4 1690.3
## + gender:transport_means                  1      0.58 5937.8 1690.3
## + test_prep:writing_score                 1      0.21 5938.1 1690.3
## + gender:lunch_type                       1      0.17 5938.2 1690.3
## - test_prep:parent_marital_status         2     60.55 5998.9 1690.3
## + lunch_type:math_score                   1      0.11 5938.2 1690.3
## + transport_means:wkly_study_hours        2     19.86 5918.5 1690.4
## - test_prep:is_first_child                1     42.31 5980.7 1690.5
## - gender:parent_educ                      5    124.51 6062.9 1690.6
## + ethnic_group:test_prep                  4     54.32 5884.0 1690.9
## - ethnic_group:transport_means            4    110.04 6048.4 1691.2
## + parent_marital_status:practice_sport    4     49.69 5888.6 1691.4
## - ethnic_group:practice_sport             8    195.12 6133.5 1691.4
## + is_first_child:wkly_study_hours         2      9.14 5929.2 1691.4
## - wkly_study_hours:math_score             2     72.30 6010.6 1691.5
## - practice_sport:writing_score            2     72.58 6010.9 1691.5
## + practice_sport:transport_means          2      7.87 5930.5 1691.6
## - gender:practice_sport                   2     73.60 6011.9 1691.6
## - lunch_type:parent_marital_status        3     94.38 6032.7 1691.7
## - wkly_study_hours:writing_score          2     80.34 6018.7 1692.3
## + parent_marital_status:transport_means   3     20.49 5917.9 1692.3
## - lunch_type:wkly_study_hours             2     81.57 6019.9 1692.4
## + parent_marital_status:math_score        3     18.57 5919.8 1692.5
## - gender:wkly_study_hours                 2     82.69 6021.0 1692.5
## - parent_educ:math_score                  5    145.08 6083.4 1692.6
## - parent_educ:test_prep                   5    145.37 6083.7 1692.6
## - is_first_child:transport_means          1     64.92 6003.3 1692.8
## - parent_marital_status:writing_score     3    106.48 6044.8 1692.8
## - ethnic_group:wkly_study_hours           8    209.94 6148.3 1692.8
## + parent_educ:transport_means             5     53.99 5884.4 1693.0
## + practice_sport:wkly_study_hours         4     31.07 5907.3 1693.2
## - parent_educ:parent_marital_status      14    347.81 6286.2 1693.9
## - transport_means:writing_score           1     78.56 6016.9 1694.1
## + parent_educ:writing_score               5     37.06 5901.3 1694.7
## + ethnic_group:is_first_child             4     14.02 5924.3 1695.0
## - practice_sport:math_score               2    112.57 6050.9 1695.4
## + parent_educ:lunch_type                  5     26.91 5911.4 1695.7
## + gender:ethnic_group                     4      5.71 5932.6 1695.8
## - parent_educ:practice_sport             10    283.33 6221.7 1695.8
## + ethnic_group:math_score                 4      3.77 5934.6 1696.0
## - ethnic_group:lunch_type                 4    169.69 6108.0 1697.0
## + parent_educ:wkly_study_hours           10    101.61 5836.7 1698.2
## - parent_marital_status:wkly_study_hours  5    212.14 6150.5 1699.1
## - ethnic_group:parent_educ               20    544.84 6483.2 1700.1
## - ethnic_group:writing_score              4    225.95 6164.3 1702.4
## - ethnic_group:parent_marital_status     10    495.30 6433.6 1715.6
## 
## Step:  AIC=1687.74
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:practice_sport + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:is_first_child + practice_sport:writing_score + 
##     practice_sport:math_score + is_first_child:transport_means + 
##     transport_means:writing_score + wkly_study_hours:writing_score + 
##     wkly_study_hours:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## - practice_sport:is_first_child           2     38.50 6011.1 1687.5
## <none>                                                5972.6 1687.7
## + is_first_child:math_score               1     19.90 5952.7 1687.8
## - gender:writing_score                    1     23.79 5996.4 1688.1
## + test_prep:practice_sport                2     34.25 5938.3 1688.3
## + is_first_child:writing_score            1     12.29 5960.3 1688.5
## + test_prep:transport_means               1     11.55 5961.0 1688.6
## + test_prep:wkly_study_hours              2     31.04 5941.5 1688.7
## + writing_score:math_score                1      8.82 5963.8 1688.9
## - gender:math_score                       1     32.56 6005.2 1689.0
## + transport_means:math_score              1      7.26 5965.3 1689.0
## + lunch_type:test_prep                    1      6.39 5966.2 1689.1
## + gender:is_first_child                   1      4.37 5968.2 1689.3
## + parent_educ:is_first_child              5     84.19 5888.4 1689.4
## + lunch_type:transport_means              1      3.66 5968.9 1689.4
## + lunch_type:practice_sport               2     23.83 5948.8 1689.4
## + lunch_type:writing_score                1      3.27 5969.3 1689.4
## + gender:parent_marital_status            3     42.30 5930.3 1689.5
## - parent_marital_status:is_first_child    2     59.11 6031.7 1689.5
## + lunch_type:is_first_child               1      1.49 5971.1 1689.6
## + gender:test_prep                        1      1.09 5971.5 1689.6
## + gender:transport_means                  1      0.93 5971.7 1689.7
## + transport_means:wkly_study_hours        2     20.98 5951.6 1689.7
## + gender:lunch_type                       1      0.32 5972.3 1689.7
## + lunch_type:math_score                   1      0.25 5972.3 1689.7
## + test_prep:math_score                    1      0.25 5972.3 1689.7
## + test_prep:writing_score                 1      0.00 5972.6 1689.7
## - test_prep:is_first_child                1     41.65 6014.2 1689.8
## - test_prep:parent_marital_status         2     62.17 6034.8 1689.8
## - ethnic_group:practice_sport             8    187.15 6159.7 1689.9
## - gender:parent_educ                      5    125.49 6098.1 1690.0
## + ethnic_group:test_prep                  4     55.00 5917.6 1690.3
## - wkly_study_hours:math_score             2     70.21 6042.8 1690.6
## + is_first_child:wkly_study_hours         2      9.83 5962.8 1690.8
## + practice_sport:transport_means          2      9.29 5963.3 1690.8
## + parent_marital_status:practice_sport    4     47.82 5924.8 1691.0
## - lunch_type:wkly_study_hours             2     74.57 6047.2 1691.1
## - parent_educ:math_score                  5    136.82 6109.4 1691.1
## - lunch_type:parent_marital_status        3     96.18 6068.8 1691.2
## - ethnic_group:transport_means            4    117.12 6089.7 1691.2
## - wkly_study_hours:writing_score          2     76.37 6049.0 1691.2
## - ethnic_group:wkly_study_hours           8    204.34 6176.9 1691.6
## + parent_marital_status:transport_means   3     21.55 5951.0 1691.6
## - practice_sport:writing_score            2     81.18 6053.8 1691.7
## - gender:wkly_study_hours                 2     81.50 6054.1 1691.7
## + parent_marital_status:math_score        3     17.83 5954.8 1692.0
## - parent_marital_status:writing_score     3    106.86 6079.5 1692.2
## - gender:practice_sport                   2     89.02 6061.6 1692.5
## - is_first_child:transport_means          1     68.79 6041.4 1692.5
## - parent_educ:test_prep                   5    152.09 6124.7 1692.6
## + parent_educ:transport_means             5     51.34 5921.3 1692.7
## + practice_sport:wkly_study_hours         4     27.53 5945.1 1693.0
## - parent_educ:parent_marital_status      14    347.67 6320.3 1693.1
## - transport_means:writing_score           1     78.81 6051.4 1693.5
## + ethnic_group:is_first_child             4     13.31 5959.3 1694.4
## + parent_educ:writing_score               5     32.53 5940.1 1694.5
## + parent_educ:lunch_type                  5     30.09 5942.5 1694.8
## + gender:ethnic_group                     4      3.93 5968.7 1695.3
## - practice_sport:math_score               2    119.00 6091.6 1695.4
## + ethnic_group:math_score                 4      3.40 5969.2 1695.4
## - ethnic_group:lunch_type                 4    161.62 6134.2 1695.5
## - parent_marital_status:wkly_study_hours  5    201.35 6173.9 1697.3
## - ethnic_group:parent_educ               20    525.54 6498.1 1697.5
## - parent_educ:practice_sport             10    314.29 6286.9 1698.0
## + parent_educ:wkly_study_hours           10     96.65 5875.9 1698.1
## - ethnic_group:writing_score              4    214.40 6187.0 1700.5
## - ethnic_group:parent_marital_status     10    493.84 6466.4 1714.6
## 
## Step:  AIC=1687.53
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + writing_score + math_score + 
##     gender:parent_educ + gender:practice_sport + gender:wkly_study_hours + 
##     gender:writing_score + gender:math_score + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + transport_means:writing_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score
## 
##                                          Df Sum of Sq    RSS    AIC
## <none>                                                6011.1 1687.5
## - gender:writing_score                    1     21.37 6032.5 1687.6
## + is_first_child:math_score               1     19.32 5991.8 1687.6
## + practice_sport:is_first_child           2     38.50 5972.6 1687.7
## - parent_marital_status:is_first_child    2     47.96 6059.0 1688.2
## - gender:math_score                       1     28.12 6039.2 1688.3
## + test_prep:transport_means               1     11.40 5999.7 1688.4
## - ethnic_group:practice_sport             8    175.00 6186.1 1688.5
## + test_prep:practice_sport                2     30.44 5980.6 1688.5
## + is_first_child:writing_score            1     10.10 6001.0 1688.5
## + test_prep:wkly_study_hours              2     29.45 5981.6 1688.6
## + writing_score:math_score                1      8.80 6002.3 1688.7
## - gender:parent_educ                      5    114.74 6125.8 1688.7
## + transport_means:math_score              1      7.25 6003.8 1688.8
## + lunch_type:test_prep                    1      7.15 6003.9 1688.8
## + gender:is_first_child                   1      5.18 6005.9 1689.0
## + lunch_type:transport_means              1      4.83 6006.3 1689.1
## + lunch_type:writing_score                1      3.41 6007.7 1689.2
## + lunch_type:practice_sport               2     23.16 5987.9 1689.2
## + gender:lunch_type                       1      1.33 6009.8 1689.4
## + transport_means:wkly_study_hours        2     21.47 5989.6 1689.4
## - test_prep:parent_marital_status         2     60.49 6071.6 1689.4
## + gender:transport_means                  1      0.90 6010.2 1689.4
## + lunch_type:is_first_child               1      0.70 6010.4 1689.5
## + gender:test_prep                        1      0.57 6010.5 1689.5
## + lunch_type:math_score                   1      0.06 6011.0 1689.5
## + test_prep:math_score                    1      0.03 6011.1 1689.5
## + test_prep:writing_score                 1      0.02 6011.1 1689.5
## + parent_educ:is_first_child              5     80.68 5930.4 1689.6
## - parent_educ:math_score                  5    123.96 6135.1 1689.6
## - test_prep:is_first_child                1     42.43 6053.5 1689.7
## + gender:parent_marital_status            3     38.29 5972.8 1689.8
## - ethnic_group:transport_means            4    107.80 6118.9 1690.0
## - wkly_study_hours:math_score             2     66.83 6077.9 1690.0
## - lunch_type:parent_marital_status        3     90.92 6102.0 1690.4
## + is_first_child:wkly_study_hours         2     10.72 6000.4 1690.5
## + parent_marital_status:practice_sport    4     50.08 5961.0 1690.6
## + ethnic_group:test_prep                  4     46.62 5964.5 1690.9
## + practice_sport:transport_means          2      5.91 6005.2 1691.0
## - wkly_study_hours:writing_score          2     78.45 6089.5 1691.2
## - practice_sport:writing_score            2     78.56 6089.7 1691.2
## - lunch_type:wkly_study_hours             2     78.96 6090.1 1691.2
## - gender:practice_sport                   2     84.25 6095.3 1691.7
## - ethnic_group:wkly_study_hours           8    210.31 6221.4 1691.8
## - gender:wkly_study_hours                 2     85.43 6096.5 1691.9
## + parent_marital_status:math_score        3     16.97 5994.1 1691.9
## - parent_educ:test_prep                   5    148.10 6159.2 1691.9
## - parent_marital_status:writing_score     3    107.18 6118.3 1692.0
## + parent_marital_status:transport_means   3     15.92 5995.2 1692.0
## - transport_means:writing_score           1     69.43 6080.5 1692.3
## - is_first_child:transport_means          1     69.60 6080.7 1692.3
## + parent_educ:transport_means             5     50.58 5960.5 1692.5
## + practice_sport:wkly_study_hours         4     25.75 5985.3 1693.0
## - parent_educ:parent_marital_status      14    351.47 6362.6 1693.1
## + parent_educ:writing_score               5     37.22 5973.9 1693.9
## + parent_educ:lunch_type                  5     36.22 5974.9 1694.0
## + ethnic_group:is_first_child             4     14.25 5996.8 1694.1
## - practice_sport:math_score               2    113.60 6124.7 1694.6
## - ethnic_group:lunch_type                 4    159.20 6170.3 1695.0
## + gender:ethnic_group                     4      3.79 6007.3 1695.2
## + ethnic_group:math_score                 4      3.63 6007.5 1695.2
## - parent_marital_status:wkly_study_hours  5    196.82 6207.9 1696.5
## - ethnic_group:parent_educ               20    528.60 6539.7 1697.3
## - parent_educ:practice_sport             10    313.80 6324.9 1697.5
## + parent_educ:wkly_study_hours           10     95.63 5915.5 1698.1
## - ethnic_group:writing_score              4    200.71 6211.8 1698.9
## - ethnic_group:parent_marital_status     10    481.20 6492.3 1713.0
summary(stepwise_model_read2)
## 
## Call:
## lm(formula = reading_score ~ gender + ethnic_group + parent_educ + 
##     lunch_type + test_prep + parent_marital_status + practice_sport + 
##     is_first_child + transport_means + wkly_study_hours + writing_score + 
##     math_score + gender:parent_educ + gender:practice_sport + 
##     gender:wkly_study_hours + gender:writing_score + gender:math_score + 
##     ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:transport_means + 
##     ethnic_group:wkly_study_hours + ethnic_group:writing_score + 
##     parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + parent_marital_status:writing_score + 
##     practice_sport:writing_score + practice_sport:math_score + 
##     is_first_child:transport_means + transport_means:writing_score + 
##     wkly_study_hours:writing_score + wkly_study_hours:math_score, 
##     data = df_4_mdl_read2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.0525 -2.1489  0.0223  2.2672  9.4698 
## 
## Coefficients: (2 not defined because of singularities)
##                                                            Estimate Std. Error
## (Intercept)                                                -2.21476    6.05325
## gendermale                                                 -0.25828    2.69120
## ethnic_groupgroup B                                         4.79875    4.43458
## ethnic_groupgroup C                                         7.75833    4.17348
## ethnic_groupgroup D                                         5.28196    4.45744
## ethnic_groupgroup E                                        -0.92056    4.68923
## parent_educbachelor's degree                               -1.34346    4.87623
## parent_educhigh school                                     -4.03417    3.68396
## parent_educmaster's degree                                -13.00825    5.55005
## parent_educsome college                                     1.51613    3.74291
## parent_educsome high school                                -7.95960    3.43483
## lunch_typestandard                                         -3.69403    1.79782
## test_prepnone                                              -1.02047    1.41570
## parent_marital_statusmarried                               -6.94406    3.65991
## parent_marital_statussingle                                -9.79338    3.97973
## parent_marital_statuswidowed                               28.09604   16.65583
## practice_sportregularly                                     4.30334    4.58906
## practice_sportsometimes                                     3.33813    4.49148
## is_first_childyes                                           0.30730    1.41663
## transport_meansschool_bus                                   1.47443    2.04096
## wkly_study_hours> 10                                        3.02830    3.69241
## wkly_study_hours10-May                                      4.27984    3.00443
## writing_score                                               0.93805    0.13802
## math_score                                                  0.17400    0.12824
## gendermale:parent_educbachelor's degree                     0.27908    1.31086
## gendermale:parent_educhigh school                          -1.37943    1.08076
## gendermale:parent_educmaster's degree                      -4.20026    1.84915
## gendermale:parent_educsome college                         -0.19030    1.09407
## gendermale:parent_educsome high school                      0.33156    1.10834
## gendermale:practice_sportregularly                          1.12615    2.02819
## gendermale:practice_sportsometimes                          3.60461    1.95233
## gendermale:wkly_study_hours> 10                            -4.31010    1.75256
## gendermale:wkly_study_hours10-May                          -1.35212    1.31064
## gendermale:writing_score                                   -0.07647    0.06178
## gendermale:math_score                                       0.08058    0.05675
## ethnic_groupgroup B:parent_educbachelor's degree            1.80093    3.33610
## ethnic_groupgroup C:parent_educbachelor's degree            3.61920    3.26168
## ethnic_groupgroup D:parent_educbachelor's degree            3.01255    3.30049
## ethnic_groupgroup E:parent_educbachelor's degree            1.35304    3.71977
## ethnic_groupgroup B:parent_educhigh school                  0.27504    2.13614
## ethnic_groupgroup C:parent_educhigh school                  1.31485    2.02529
## ethnic_groupgroup D:parent_educhigh school                  0.28283    2.11737
## ethnic_groupgroup E:parent_educhigh school                  2.38191    2.35845
## ethnic_groupgroup B:parent_educmaster's degree             13.22752    4.04855
## ethnic_groupgroup C:parent_educmaster's degree             12.37096    3.84183
## ethnic_groupgroup D:parent_educmaster's degree              6.87697    3.74574
## ethnic_groupgroup E:parent_educmaster's degree              9.75762    4.16976
## ethnic_groupgroup B:parent_educsome college                 0.64794    2.40932
## ethnic_groupgroup C:parent_educsome college                 1.02442    2.24934
## ethnic_groupgroup D:parent_educsome college                 1.15477    2.37057
## ethnic_groupgroup E:parent_educsome college                 5.34836    2.43228
## ethnic_groupgroup B:parent_educsome high school             4.69093    2.23947
## ethnic_groupgroup C:parent_educsome high school             3.70174    2.18437
## ethnic_groupgroup D:parent_educsome high school             2.87097    2.19681
## ethnic_groupgroup E:parent_educsome high school             7.73872    2.39189
## ethnic_groupgroup B:lunch_typestandard                      2.86667    1.58361
## ethnic_groupgroup C:lunch_typestandard                      3.91173    1.52070
## ethnic_groupgroup D:lunch_typestandard                      4.79843    1.54487
## ethnic_groupgroup E:lunch_typestandard                      2.62414    1.70699
## ethnic_groupgroup B:parent_marital_statusmarried            7.40685    2.18629
## ethnic_groupgroup C:parent_marital_statusmarried            3.87793    2.10062
## ethnic_groupgroup D:parent_marital_statusmarried            2.25615    2.04995
## ethnic_groupgroup E:parent_marital_statusmarried            4.58007    2.26496
## ethnic_groupgroup B:parent_marital_statussingle             9.07991    2.54779
## ethnic_groupgroup C:parent_marital_statussingle             5.97661    2.44902
## ethnic_groupgroup D:parent_marital_statussingle             6.45149    2.41769
## ethnic_groupgroup E:parent_marital_statussingle            10.72172    2.71864
## ethnic_groupgroup B:parent_marital_statuswidowed           -3.80756   18.56512
## ethnic_groupgroup C:parent_marital_statuswidowed            7.46402   30.50690
## ethnic_groupgroup D:parent_marital_statuswidowed          -13.26686   14.72030
## ethnic_groupgroup E:parent_marital_statuswidowed                 NA         NA
## ethnic_groupgroup B:practice_sportregularly                -3.83286    2.80925
## ethnic_groupgroup C:practice_sportregularly                -5.49412    2.69971
## ethnic_groupgroup D:practice_sportregularly                -4.87583    2.86891
## ethnic_groupgroup E:practice_sportregularly                -0.94415    2.90183
## ethnic_groupgroup B:practice_sportsometimes                -2.14747    2.95073
## ethnic_groupgroup C:practice_sportsometimes                -3.63355    2.82067
## ethnic_groupgroup D:practice_sportsometimes                -4.66182    3.00407
## ethnic_groupgroup E:practice_sportsometimes                -0.92256    2.96174
## ethnic_groupgroup B:transport_meansschool_bus              -0.42056    1.57754
## ethnic_groupgroup C:transport_meansschool_bus               0.60605    1.45416
## ethnic_groupgroup D:transport_meansschool_bus               2.38901    1.50959
## ethnic_groupgroup E:transport_meansschool_bus               1.62760    1.67793
## ethnic_groupgroup B:wkly_study_hours> 10                   -1.89818    2.52835
## ethnic_groupgroup C:wkly_study_hours> 10                   -1.51105    2.49342
## ethnic_groupgroup D:wkly_study_hours> 10                   -4.02474    2.49719
## ethnic_groupgroup E:wkly_study_hours> 10                   -2.66490    2.66132
## ethnic_groupgroup B:wkly_study_hours10-May                 -1.05320    2.17191
## ethnic_groupgroup C:wkly_study_hours10-May                 -2.75061    2.14577
## ethnic_groupgroup D:wkly_study_hours10-May                 -3.83976    2.18461
## ethnic_groupgroup E:wkly_study_hours10-May                 -5.25480    2.37169
## ethnic_groupgroup B:writing_score                          -0.16442    0.04847
## ethnic_groupgroup C:writing_score                          -0.16444    0.04776
## ethnic_groupgroup D:writing_score                          -0.12672    0.04778
## ethnic_groupgroup E:writing_score                          -0.10342    0.05396
## parent_educbachelor's degree:test_prepnone                 -1.00503    1.27661
## parent_educhigh school:test_prepnone                        1.01928    1.16640
## parent_educmaster's degree:test_prepnone                    4.60672    1.96432
## parent_educsome college:test_prepnone                      -1.17611    1.15786
## parent_educsome high school:test_prepnone                   0.35747    1.10318
## parent_educbachelor's degree:parent_marital_statusmarried  -2.18740    2.33245
## parent_educhigh school:parent_marital_statusmarried         1.80301    1.65539
## parent_educmaster's degree:parent_marital_statusmarried    -6.30035    2.35025
## parent_educsome college:parent_marital_statusmarried       -1.88890    1.58412
## parent_educsome high school:parent_marital_statusmarried   -0.76985    1.56287
## parent_educbachelor's degree:parent_marital_statussingle   -0.87797    2.65282
## parent_educhigh school:parent_marital_statussingle          1.27707    1.82206
## parent_educmaster's degree:parent_marital_statussingle     -2.48327    2.42624
## parent_educsome college:parent_marital_statussingle        -1.12806    1.78648
## parent_educsome high school:parent_marital_statussingle     1.75508    1.74397
## parent_educbachelor's degree:parent_marital_statuswidowed  13.67748   13.51473
## parent_educhigh school:parent_marital_statuswidowed       -16.26360   16.73436
## parent_educmaster's degree:parent_marital_statuswidowed   -14.68575   15.60756
## parent_educsome college:parent_marital_statuswidowed        6.06937   19.94302
## parent_educsome high school:parent_marital_statuswidowed   -0.90945   11.16785
## parent_educbachelor's degree:practice_sportregularly       -3.83925    2.38818
## parent_educhigh school:practice_sportregularly             -1.53783    1.97962
## parent_educmaster's degree:practice_sportregularly          0.02556    2.73642
## parent_educsome college:practice_sportregularly             1.60463    2.03344
## parent_educsome high school:practice_sportregularly        -0.36100    1.88111
## parent_educbachelor's degree:practice_sportsometimes       -3.59853    2.33333
## parent_educhigh school:practice_sportsometimes             -0.60209    1.90898
## parent_educmaster's degree:practice_sportsometimes         -1.52626    2.50252
## parent_educsome college:practice_sportsometimes             0.48721    1.97873
## parent_educsome high school:practice_sportsometimes         3.04852    1.80284
## parent_educbachelor's degree:math_score                     0.05130    0.04414
## parent_educhigh school:math_score                           0.04416    0.03800
## parent_educmaster's degree:math_score                       0.08309    0.06234
## parent_educsome college:math_score                         -0.03771    0.03788
## parent_educsome high school:math_score                      0.05039    0.03615
## lunch_typestandard:parent_marital_statusmarried            -0.92594    1.13379
## lunch_typestandard:parent_marital_statussingle              0.40177    1.31966
## lunch_typestandard:parent_marital_statuswidowed            15.42081    7.73865
## lunch_typestandard:wkly_study_hours> 10                     1.52484    1.30358
## lunch_typestandard:wkly_study_hours10-May                  -1.09665    0.97682
## test_prepnone:parent_marital_statusmarried                  2.40484    1.16596
## test_prepnone:parent_marital_statussingle                   2.25693    1.31817
## test_prepnone:parent_marital_statuswidowed                -15.88908   13.47017
## test_prepnone:is_first_childyes                             1.39949    0.80241
## parent_marital_statusmarried:is_first_childyes             -2.23441    1.27424
## parent_marital_statussingle:is_first_childyes              -1.37971    1.40260
## parent_marital_statuswidowed:is_first_childyes             16.48409   11.02305
## parent_marital_statusmarried:wkly_study_hours> 10           2.85843    1.75319
## parent_marital_statussingle:wkly_study_hours> 10            4.02397    1.93428
## parent_marital_statuswidowed:wkly_study_hours> 10          10.22989   13.47410
## parent_marital_statusmarried:wkly_study_hours10-May        -1.02820    1.23023
## parent_marital_statussingle:wkly_study_hours10-May         -2.19040    1.37506
## parent_marital_statuswidowed:wkly_study_hours10-May              NA         NA
## parent_marital_statusmarried:writing_score                  0.06963    0.04155
## parent_marital_statussingle:writing_score                   0.04234    0.04633
## parent_marital_statuswidowed:writing_score                 -0.45567    0.24320
## practice_sportregularly:writing_score                       0.16580    0.12044
## practice_sportsometimes:writing_score                       0.25955    0.11670
## practice_sportregularly:math_score                         -0.20664    0.12037
## practice_sportsometimes:math_score                         -0.30668    0.11525
## is_first_childyes:transport_meansschool_bus                 1.78661    0.79975
## transport_meansschool_bus:writing_score                    -0.05318    0.02383
## wkly_study_hours> 10:writing_score                         -0.21770    0.09572
## wkly_study_hours10-May:writing_score                       -0.11246    0.06877
## wkly_study_hours> 10:math_score                             0.18527    0.09508
## wkly_study_hours10-May:math_score                           0.13290    0.07180
##                                                           t value Pr(>|t|)    
## (Intercept)                                                -0.366 0.714635    
## gendermale                                                 -0.096 0.923586    
## ethnic_groupgroup B                                         1.082 0.279804    
## ethnic_groupgroup C                                         1.859 0.063715 .  
## ethnic_groupgroup D                                         1.185 0.236680    
## ethnic_groupgroup E                                        -0.196 0.844457    
## parent_educbachelor's degree                               -0.276 0.783056    
## parent_educhigh school                                     -1.095 0.274101    
## parent_educmaster's degree                                 -2.344 0.019541 *  
## parent_educsome college                                     0.405 0.685630    
## parent_educsome high school                                -2.317 0.020954 *  
## lunch_typestandard                                         -2.055 0.040508 *  
## test_prepnone                                              -0.721 0.471406    
## parent_marital_statusmarried                               -1.897 0.058453 .  
## parent_marital_statussingle                                -2.461 0.014253 *  
## parent_marital_statuswidowed                                1.687 0.092354 .  
## practice_sportregularly                                     0.938 0.348904    
## practice_sportsometimes                                     0.743 0.457757    
## is_first_childyes                                           0.217 0.828370    
## transport_meansschool_bus                                   0.722 0.470429    
## wkly_study_hours> 10                                        0.820 0.412589    
## wkly_study_hours10-May                                      1.425 0.155023    
## writing_score                                               6.796 3.58e-11 ***
## math_score                                                  1.357 0.175554    
## gendermale:parent_educbachelor's degree                     0.213 0.831506    
## gendermale:parent_educhigh school                          -1.276 0.202518    
## gendermale:parent_educmaster's degree                      -2.271 0.023612 *  
## gendermale:parent_educsome college                         -0.174 0.861998    
## gendermale:parent_educsome high school                      0.299 0.764972    
## gendermale:practice_sportregularly                          0.555 0.579014    
## gendermale:practice_sportsometimes                          1.846 0.065532 .  
## gendermale:wkly_study_hours> 10                            -2.459 0.014312 *  
## gendermale:wkly_study_hours10-May                          -1.032 0.302813    
## gendermale:writing_score                                   -1.238 0.216467    
## gendermale:math_score                                       1.420 0.156384    
## ethnic_groupgroup B:parent_educbachelor's degree            0.540 0.589592    
## ethnic_groupgroup C:parent_educbachelor's degree            1.110 0.267785    
## ethnic_groupgroup D:parent_educbachelor's degree            0.913 0.361879    
## ethnic_groupgroup E:parent_educbachelor's degree            0.364 0.716227    
## ethnic_groupgroup B:parent_educhigh school                  0.129 0.897611    
## ethnic_groupgroup C:parent_educhigh school                  0.649 0.516546    
## ethnic_groupgroup D:parent_educhigh school                  0.134 0.893800    
## ethnic_groupgroup E:parent_educhigh school                  1.010 0.313087    
## ethnic_groupgroup B:parent_educmaster's degree              3.267 0.001173 ** 
## ethnic_groupgroup C:parent_educmaster's degree              3.220 0.001379 ** 
## ethnic_groupgroup D:parent_educmaster's degree              1.836 0.067055 .  
## ethnic_groupgroup E:parent_educmaster's degree              2.340 0.019734 *  
## ethnic_groupgroup B:parent_educsome college                 0.269 0.788111    
## ethnic_groupgroup C:parent_educsome college                 0.455 0.649028    
## ethnic_groupgroup D:parent_educsome college                 0.487 0.626415    
## ethnic_groupgroup E:parent_educsome college                 2.199 0.028415 *  
## ethnic_groupgroup B:parent_educsome high school             2.095 0.036784 *  
## ethnic_groupgroup C:parent_educsome high school             1.695 0.090864 .  
## ethnic_groupgroup D:parent_educsome high school             1.307 0.191949    
## ethnic_groupgroup E:parent_educsome high school             3.235 0.001308 ** 
## ethnic_groupgroup B:lunch_typestandard                      1.810 0.070959 .  
## ethnic_groupgroup C:lunch_typestandard                      2.572 0.010436 *  
## ethnic_groupgroup D:lunch_typestandard                      3.106 0.002021 ** 
## ethnic_groupgroup E:lunch_typestandard                      1.537 0.124956    
## ethnic_groupgroup B:parent_marital_statusmarried            3.388 0.000769 ***
## ethnic_groupgroup C:parent_marital_statusmarried            1.846 0.065565 .  
## ethnic_groupgroup D:parent_marital_statusmarried            1.101 0.271690    
## ethnic_groupgroup E:parent_marital_statusmarried            2.022 0.043779 *  
## ethnic_groupgroup B:parent_marital_statussingle             3.564 0.000406 ***
## ethnic_groupgroup C:parent_marital_statussingle             2.440 0.015072 *  
## ethnic_groupgroup D:parent_marital_statussingle             2.668 0.007908 ** 
## ethnic_groupgroup E:parent_marital_statussingle             3.944 9.36e-05 ***
## ethnic_groupgroup B:parent_marital_statuswidowed           -0.205 0.837597    
## ethnic_groupgroup C:parent_marital_statuswidowed            0.245 0.806831    
## ethnic_groupgroup D:parent_marital_statuswidowed           -0.901 0.367952    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                -1.364 0.173163    
## ethnic_groupgroup C:practice_sportregularly                -2.035 0.042454 *  
## ethnic_groupgroup D:practice_sportregularly                -1.700 0.089938 .  
## ethnic_groupgroup E:practice_sportregularly                -0.325 0.745065    
## ethnic_groupgroup B:practice_sportsometimes                -0.728 0.467145    
## ethnic_groupgroup C:practice_sportsometimes                -1.288 0.198372    
## ethnic_groupgroup D:practice_sportsometimes                -1.552 0.121435    
## ethnic_groupgroup E:practice_sportsometimes                -0.311 0.755577    
## ethnic_groupgroup B:transport_meansschool_bus              -0.267 0.789910    
## ethnic_groupgroup C:transport_meansschool_bus               0.417 0.677056    
## ethnic_groupgroup D:transport_meansschool_bus               1.583 0.114256    
## ethnic_groupgroup E:transport_meansschool_bus               0.970 0.332588    
## ethnic_groupgroup B:wkly_study_hours> 10                   -0.751 0.453209    
## ethnic_groupgroup C:wkly_study_hours> 10                   -0.606 0.544823    
## ethnic_groupgroup D:wkly_study_hours> 10                   -1.612 0.107758    
## ethnic_groupgroup E:wkly_study_hours> 10                   -1.001 0.317222    
## ethnic_groupgroup B:wkly_study_hours10-May                 -0.485 0.627981    
## ethnic_groupgroup C:wkly_study_hours10-May                 -1.282 0.200576    
## ethnic_groupgroup D:wkly_study_hours10-May                 -1.758 0.079518 .  
## ethnic_groupgroup E:wkly_study_hours10-May                 -2.216 0.027238 *  
## ethnic_groupgroup B:writing_score                          -3.392 0.000758 ***
## ethnic_groupgroup C:writing_score                          -3.443 0.000632 ***
## ethnic_groupgroup D:writing_score                          -2.652 0.008299 ** 
## ethnic_groupgroup E:writing_score                          -1.917 0.055948 .  
## parent_educbachelor's degree:test_prepnone                 -0.787 0.431560    
## parent_educhigh school:test_prepnone                        0.874 0.382675    
## parent_educmaster's degree:test_prepnone                    2.345 0.019470 *  
## parent_educsome college:test_prepnone                      -1.016 0.310315    
## parent_educsome high school:test_prepnone                   0.324 0.746067    
## parent_educbachelor's degree:parent_marital_statusmarried  -0.938 0.348866    
## parent_educhigh school:parent_marital_statusmarried         1.089 0.276685    
## parent_educmaster's degree:parent_marital_statusmarried    -2.681 0.007628 ** 
## parent_educsome college:parent_marital_statusmarried       -1.192 0.233760    
## parent_educsome high school:parent_marital_statusmarried   -0.493 0.622556    
## parent_educbachelor's degree:parent_marital_statussingle   -0.331 0.740837    
## parent_educhigh school:parent_marital_statussingle          0.701 0.483747    
## parent_educmaster's degree:parent_marital_statussingle     -1.024 0.306644    
## parent_educsome college:parent_marital_statussingle        -0.631 0.528086    
## parent_educsome high school:parent_marital_statussingle     1.006 0.314802    
## parent_educbachelor's degree:parent_marital_statuswidowed   1.012 0.312086    
## parent_educhigh school:parent_marital_statuswidowed        -0.972 0.331661    
## parent_educmaster's degree:parent_marital_statuswidowed    -0.941 0.347264    
## parent_educsome college:parent_marital_statuswidowed        0.304 0.761019    
## parent_educsome high school:parent_marital_statuswidowed   -0.081 0.935134    
## parent_educbachelor's degree:practice_sportregularly       -1.608 0.108655    
## parent_educhigh school:practice_sportregularly             -0.777 0.437685    
## parent_educmaster's degree:practice_sportregularly          0.009 0.992553    
## parent_educsome college:practice_sportregularly             0.789 0.430474    
## parent_educsome high school:practice_sportregularly        -0.192 0.847906    
## parent_educbachelor's degree:practice_sportsometimes       -1.542 0.123752    
## parent_educhigh school:practice_sportsometimes             -0.315 0.752610    
## parent_educmaster's degree:practice_sportsometimes         -0.610 0.542257    
## parent_educsome college:practice_sportsometimes             0.246 0.805627    
## parent_educsome high school:practice_sportsometimes         1.691 0.091568 .  
## parent_educbachelor's degree:math_score                     1.162 0.245837    
## parent_educhigh school:math_score                           1.162 0.245750    
## parent_educmaster's degree:math_score                       1.333 0.183327    
## parent_educsome college:math_score                         -0.995 0.320060    
## parent_educsome high school:math_score                      1.394 0.164075    
## lunch_typestandard:parent_marital_statusmarried            -0.817 0.414564    
## lunch_typestandard:parent_marital_statussingle              0.304 0.760929    
## lunch_typestandard:parent_marital_statuswidowed             1.993 0.046924 *  
## lunch_typestandard:wkly_study_hours> 10                     1.170 0.242756    
## lunch_typestandard:wkly_study_hours10-May                  -1.123 0.262202    
## test_prepnone:parent_marital_statusmarried                  2.063 0.039755 *  
## test_prepnone:parent_marital_statussingle                   1.712 0.087585 .  
## test_prepnone:parent_marital_statuswidowed                 -1.180 0.238820    
## test_prepnone:is_first_childyes                             1.744 0.081852 .  
## parent_marital_statusmarried:is_first_childyes             -1.754 0.080222 .  
## parent_marital_statussingle:is_first_childyes              -0.984 0.325824    
## parent_marital_statuswidowed:is_first_childyes              1.495 0.135537    
## parent_marital_statusmarried:wkly_study_hours> 10           1.630 0.103744    
## parent_marital_statussingle:wkly_study_hours> 10            2.080 0.038084 *  
## parent_marital_statuswidowed:wkly_study_hours> 10           0.759 0.448132    
## parent_marital_statusmarried:wkly_study_hours10-May        -0.836 0.403744    
## parent_marital_statussingle:wkly_study_hours10-May         -1.593 0.111906    
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## parent_marital_statusmarried:writing_score                  1.676 0.094490 .  
## parent_marital_statussingle:writing_score                   0.914 0.361268    
## parent_marital_statuswidowed:writing_score                 -1.874 0.061660 .  
## practice_sportregularly:writing_score                       1.377 0.169355    
## practice_sportsometimes:writing_score                       2.224 0.026653 *  
## practice_sportregularly:math_score                         -1.717 0.086742 .  
## practice_sportsometimes:math_score                         -2.661 0.008083 ** 
## is_first_childyes:transport_meansschool_bus                 2.234 0.025997 *  
## transport_meansschool_bus:writing_score                    -2.231 0.026183 *  
## wkly_study_hours> 10:writing_score                         -2.274 0.023437 *  
## wkly_study_hours10-May:writing_score                       -1.635 0.102739    
## wkly_study_hours> 10:math_score                             1.948 0.052008 .  
## wkly_study_hours10-May:math_score                           1.851 0.064862 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.735 on 431 degrees of freedom
## Multiple R-squared:  0.9555, Adjusted R-squared:  0.9392 
## F-statistic:  58.6 on 158 and 431 DF,  p-value: < 2.2e-16